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ATE OF MORTALITY! 



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JONES. 



1 — 

LIBRARY 

OF THE -"^^ 

UNIVERSITY OF CALIFORNIA. 

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Chus 




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A 



SERIES OF TABLES 



OF 



ANNUITIES AND ASSURANCES 



CALCULATED FROM 



NEW RATE OF MOETALITT 



T 



AMONGST 



ASSURED LIVES: 

WITH 

EXAMPLES 

ILLUSTRATIVE OF THEIR CONSTRUCTION AND APPLICATION, 

&c. &c. &c. 



BY 

JENKIN JONES, 

ACTUARY TO THE NATIONAL MERCANTILE LIFE ASSURANCE SOCIETY 



LONDON 



PUBLISHED BY LONGMAN, BROWN, GREEN k. LONGMANS; 

AND JONES & CAUSTON, 47, EASTCHEAP. 

EDINBURGH: A. & C. BLACK. 



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V^G- ^47 



PRINTED BT JONES AND CAUSTOW, 47, EASTCHEAP, LONDON . 



PHEFACE. 



The object of the present publication, and an 
explanation of the data, from which the Tables have 
been computed, are set forth in the " Introduction/' 

It was originally the Author's intention simply to 
publish a few Tables, with practical examples, illus- 
trative of their application ; but, in working out the 
examples, it occurred to him that it would not be 
unacceptable to those who take an interest in 
the subject, but who are not familiar with the theory 
of Annuities and Assurances, if he were also to 
explain, without using any Algebraic symbols, the 
principles upon which the Tables were constructed. 
This he has endeavoured to accomplish. 

To those persons, therefore, who are acquainted 
with decimal arithmetic, the author thinks that they 
would find in the '^ Examples'" an ^' Elementary 
Treatise" on Annuities and Assurances, which would 
be of considerable service to them by way of prepa- 
ration for the study of the larger and more compre- 
hensive treatises by Milne, Bailey, and D, Jones. 

The whole of the computations made from the 
'' New Rate of Mortality," have been carefully cal- 
culated by two separate computers 

In the construction of some of the Tables, the 



11 



Author is indebted to Mr. Joseph J. Cleghorn, the 
efficient Deputy to Mr. Griffith Davies, the Actuary 
of the Guardian Assurance Company^ who had pre- 
viously computed them for the use of his own office, 
and which, upon comparison, were found to agree in 
every respect with those computed by the Author. 

The Author is also indebted to Mr. Griffith Davies^ 
step-son, Mr. Evan Owen Glynne of the Legal and 
General Life Office, whose services he was fortunate 
enough to obtain, and by whom the greater portion 
of the calculations were made in Duplicate with the 
Author. 

The Legal Decisions were compiled by the Author's 
friend, Mr. Hugh Owen, of the Poor Law Commis- 
sion Office. 

The Author had intended to print, by way of 
Appendix, a Popular Exposition of the Principles of 
Assurance, with observations upon the various '^ad- 
vantages'' held out by the several Life Offices, and 
a comparison of their rates of premium, &c., but it 
has been suggested to him that it would be desirable 
to make a separate, and a very cheap publication of 
it, which the author purposes doing at a future 
opportunity. 



National Mercantile 

Life Assurance Society, 

December "11, 1843. 



CONTENTS. 



Paste 
PREFACE. 

INTRODUCTION. 

EXAMPLES ILLUSTRATIVE OF 

Compound Interest, 

Definition of, , , \ 

To find the Amount of Sums at, 2 

Deferred Sums certain, 

Definition of, 4 

To find the Present Values of, 5 

Annuities certain, 

Amounts of, 5 

Present Values of, 9 

Immediate, 9 

Perpetual, 11 

Deferred, 12 

New Rate of Mortality, ., 14 

Probabilities of Life, , 15 

To find the probability of a Life surviving any Age, 18 

Do. Do. failing in any year of Age, 18 

To determine the number and amount of claims that a Life 

Office may expect in a year, 18 

To find the probability of two Lives surviving a term of years, 20 

Expectation of Life 

Definition of, 21 

Mode of constructing Table of, 21 

Comparative Expectations of Life, 23 

Life Annuities and Assurances: 

Construction of D, N, M, &c. columns, 24 

To determine the value of Annuities by the D and N columns, 27 

Do. do. Premiums for Assurances by D and 

M columns, 31 



Page 
EXAMPLES ILLUSTRATIVE OF 
Life Annuities, 

Single Lives— Ho determine the value of an Annuity by the 

ordinary method, 32 

Joint Lives, ditto, ditto, ditto, 34 

Two Joint Lives, and the Survivor, ditto ditto, 37 

Absolute Reversions : 

Present Values, 38 

Life Assurances, 

Single Lives — Ordinary method of determining Premiums, fur 39 
Joint Lives, Ditto ditto,' 43 

Last Survivor, Ditto ditto, 45 

Valuation of Policies : 

Construction of Preparatory Tables for, 47 

What is the value of a Policy 48 

Temporary Annuities and Assurances : 

Comparison of the D, N, &c. method and ordinary method 
of calculating values of, 51 

TABLES : 

Compound Interest — Amounts, !• 

Deferred Sums certain — Present Values, II. 

Annuities certain — Amounts, ' * HI- 

Do. Present Values IV. 

New Rate of Mortality, V. 

Probabilities of Life, VI- 

Expectation of Life VU* 

Comparative Expectations of Life, VIIT. 

D, N, S, M, and R, columns, 

2i per Cent IX. 

3 „ X. 

3^ „ XL 

Life Annuities — Single Lives, XII. 

Do. Joint Lives, XIII. 

Absolute Reversions — Present Values, XIV. 

Life Assurances— Single Lives— Single and Annual Premiums,. . XV. 

Do. Joint do. do. XVI. 

Do. Last Survivor, do. XVII. 

Valuation of Policies— Preparatory Tables : 

Annuities 3 per Cent. — Interpolated for Months, XVIII. 

Single Premiums, do. — Do. XIX. 

LEGAL DECISIONS. 



INTRODUCTION. 



The institution of Life Assurance Societies is 
generally admitted to be one of the most important 
and benevolent features in modern civilization : and 
it must be gratifying to all who take an interest in 
the welfare of society and in the happiness of their 
species^ to observe the great increase which has 
taken place in the number of these institutions so 
far as that fact may be taken as an indication of the 
increase in the numbers who have availed themselves 
of their advantages. The great danger^ however, 
is that by over competition parties may be (as 
some have been) induced to charge premiums which 
are too low to cover the risks incurred, and thus be 
productive of the very mischief which it is ostensibly 
their object to prevent. 

The great importance of the subject will be 
manifest when it is considered that thousands of 
persons are annually investing a large portion of their 
income to provide subsistence for their families, in the 

c 



IV. INTRODUCTION. 

event of their own premature death, and that a very 
large portion of the property of the country is depen- 
dent upon the tenure of human life, so that the welfare 
and future happiness of a large part of the commu- 
nity are entirely dependent upon the solvency of 
these institutions. It is therefore of the first im- 
portance that the tables of rates should be calculated 
from the most recent and most extensive experience 
that can be obtained ; so that, on the one hand, they 
should not be exorbitant; yet, on the other, that 
they should he fully adequate to cover the risks, and 
to meet all the liabilities incurred. 

To determine the premiums, single or periodical, 
which ought to be charged for any description of 
assurance, it is first necessary to construct a table of 
mortality — that is, a table exhibiting out of a certain 
number born or who complete a given age, say 1 00,000, 
the number who die in each year of age, from birth, or 
the given age to the extreme of life. It is by means 
of such a table, combined with the interest of money, 
that the premiums charged by Life Offices are 
determined. 

The earlier societies, such as the Amicable, and 
Royal Exchange, which were established in the 
] 7th century, it appears, charged a premium of £5 
per cent., on all lives assured without reference 
to age\ but it is needless to add that they have since 
adopted proportionate rates for the risk of each age ; 
and in the absence of better materials the premiums 
charged by the Equitable Life Office were deduced 



INTRODUCTION. V 

from the probabilities of life in London during a 
period of 20 years^ which included the year 1740, 
when the mortality was considered to be almost 
equal to that of a plague. These premiums, how- 
ever, were not deemed by the then Attorney-General 
to be sufficiently high, and the Crown, in consequence 
of his recommendation, refused to issue a charter, 
which naturally retarded very materially the progress 
of the society. 

In the year 1776, however, the premiums were 
reduced 1- 10th, and in 1 780, Dr. Price's Northampton 
Table was adopted as the basis upon which a fresh 
set of rates was calculated, to which 15 per cent, 
was added for further security. This, however, was 
taken off in 1785, and the premiums from that date 
to the present have remained unaltered. 

The Northampton Table was formed by Dr. Price 
from bills of the mortality during the years 1735 to 
1780, in the parish of All Saints, Northampton, 
which contained little more than half the popula- 
tion of that town, and on the supposition of a sta- 
tionary population, whereas the population was 
then increasing. It is manifest that a rate of 
mortality so obtained and deduced from the experi- 
ence of one parish could not be taken as an index of 
the mortality throughout the kingdom, which con- 
tains upwards of 12,000 parishes. This, however, 
is the table used by the majority of the old Life 
Offices, and by some of the new, although it has 
apparently been proved^ at least by the experience 



VI 



INTRODUCTION. 



of the Equitable, to represent the mortality much 
too high, especially at the younger and middle ages. 
This will be seen by the following table extracted 
from Mr. Morgan's " View of the rise and progress 
of the Equitable Society/' which shews the num- 
ber who died in the 12 years preceding 1829, 
out of a certain number of assurances in force, and 
contrasts that number with the number that they 
had reason, according to the Northampton rate to 
expect to have died in that period. 



Age. 


No. 


Died. 


Should 
have died. 


20 to 30 


4720 


29 


68 


30 n 40 


15951 


106 


243 


40 // 50 


27072 


201 


506 


60 t 60 


23307 


339 


545 


60 n 70 


14705 


426 


502 


70 // 80 


5056 


289 


290 


80 // 95 


701 


99 


94 



Various other tables of mortality have been con- 
structed since the Northampton : of those of most 
note the first is the Swedish, which was constructed 
from returns collected in the years from 1 755 to 1776, 
inclusively, and which contained the whole population 
of Sweden and Finland. This Table has been since 
corrected from more recent data. The next is a 
table by Mons. De Parcieux exhibiting the mortality 
among-st the nominees of the French Tontine. The 
more recent tables, and those now generally 
used are the Carlisle and Equitable rates of mor- 



INTRODUCTION. Vll 



tality. The Carlisle was framed by Mr. Milne, from 
observations made by Dr Heysham, of the mortality 
in that town during the years 1779-1787, upon a 
population of 8,000 persons. The " Equitable" was 
framed by Mr. Griffith Davies, from the decrements 
of life among the members at the Equitable, and 
subsequently by Mr. Morgan, from more complete 
data, so that Mr. Davies' table can now only be 
considered as a graduated Carlisle. 

The Carlisle table agrees very closely with the 
Equitable, but independently of the objection to a 
table based upon so few observations, it will be found, 
notwithstanding its close agreement with the Equi- 
table experience, that for the want of a greater 
number of observations at each age, and the table 
not being graduated, but confined strictly to the 
data afforded at each age, the Carlisle is imprac- 
ticable as a basis for temporary assurances, for, on 
account of the irregularities in the probabilities of 
dying in one year at several of the ages, the pre- 
miums deduced therefrom would, in some instances, 
be greater for young lives than for old ones. For 
example — at 45 the premium to assure ^1000 for 
one year would he £\4 8s. Or/., and at 50 it would 
be .^'IS Os. Od. The irregularities in the probabilities 
would also affect survivorship assurances, as the 
probability of surviving one year is an important 
element in the calculation of those contingencies. 

Mr. Milne states that the Carlisle table differs very 
little from the general law that obtains throughout 



Vlll INTRODUCTION. 

the country, taking town and country together. But 
supposing the Carlisle, or any other table, to repre- 
sent accurately the mortality of the united kingdom, 
such a rate ought only to be used in the absence of 
the actual experience of the mortality amongst 
assured lives, for offices do not take lives indiscrimi- 
nately, but have the power of selection. Now if an 
office is prudently conducted, all doubtful lives are 
rejected; andif it were possible to select all good lives 
such a table as the Carlisle would manifestly repre- 
sent a mortality higher than that which would pre- 
vail amongst the lives actually assured. As there 
is also greater laxity in the selection of lives in some 
offices than in others, and as it will happen, even 
with the utmost vigilance exercised, that some 
unsound lives will be passed as eligible, it is manifest 
that a rate of mortality, deduced from the combined 
experience of the various Life Offices, is the most 
consistent, and the safest basis upon which the rates 
of assurance ought to be determined. 

Mr. Griffith Davies, the able and experienced 
Actuary of the Guardian Life Office, in his observa- 
tions upon the data afforded by the Equitable 
observes, — '"^ It must be allowed that however 
doubtful the limited experience of a new institution 
might be regarded, the proportions stated by Mr. 
Morgan, repeated and confirmed as they have been for 
a period exceeding half a century, afford more satis- 
factory data for determining the rate of mortality among 
assuredlives, than any registers hitherto made public.'' 



INTRODUCTION. IX 

Mr. Babbage, in his " Comparative view of the 
various Institutions for the Assurance of Lives/' says^ 
in reference to the best data for constructing a rate 
of mortality, that ^' It is, therefore, to be expected 
that the law of mortality which exists amongst 
assurers, should approach more nearly to that 
which takes place amongst select classes of mankind, 
such as amongst annuitants, (where it is the interest 
of each proprietor to select a good life) than to more 
indiscriminate bodies of people. Although there exist 
good observations of this kind, I am not aware of 
their having been employed as the basis of any 
table of premiums for assurances.'^ 

^' Having now pointed out the defects of the tables 
in general use, it will naturally be inquired what 
others it is proposed to substitute. To this it may 
be answered, that the best substitution would be a 
table actually constructed from the deaths occurring 
amongst a large body of persons of this very class 
whose law of mortality we wish to ascertain. Mate- 
rials for such a table exist, and probably in the best 
and most authentic form. The Equitable Society has 
been established sixty years, and it must possess 
records of the death, and cause of death, of all those 
who have had claims on its funds. Another society 
of considerable extent, the Amicable, has existed 
above a century, a vast quantity of valuable mate- 
rials is, without doubt, contained in the records of 
these two societies, and if they were each to com- 
municate to the public the facts of which they 



INTRODUCTION. 



are in possession, it would form a most important 
addition to our knowledge, and supply the most 
accurate materials for tables of this class which have 
yet been produced/^ 

By the liberality of several of the Life Offices, and 
the disinterested zeal and services of a Committee of 
some of the most experienced and eminent of the 
Actuaries, we have now^ data for the construction of 
a rate of mortality, not simply of the experience of the 
Equitable and Amicable, but of the combined expe- 
rience of no less than 17^ Life Offices, embracing 
83,905 policies, and a rate of mortality has been 
adjusted by one of the most eminent Mathematicians 
on the Committee, from the combined town and 
country experience, embracing 62,537 assurances. 

It is a very common practice with some of the 
offices to announce their premiums as having been 
computed by an able Mathematician from the 
most recent and most extensive experience, without 
usually stating what such experience is, or giving the 
name of the able Mathematician, who is thus alleged 
to have constructed their tables. As, however, we 
have now very recent and extensive experience of the 

* It may not be amiss here to observe that 13, out of the 17, contribu- 
ting offices are proprietary companies, who would thus appear to be 
animated by motives equally as disinterested as those of the " Equitable" 
and " Amicable," who, as Mr. Babbage observes, " have no private 
interests to oppose their publishing for the advancement of science, the 
results of that experience which it alone, by securing their stability, has 
enabled them to acquire, thus supplying the solid materials of further 
improvements, which must inevitably reflect back the greatest advan- 
ages on those most largely engaged in such transactions." 



INTRODUCTION. 



XI 



mortality amongst assured lives^ such as ought to 
form the basis upon which all rates shall in 
future be calculated, it may be useful to explain 
the origin of the Committee, and the course adopted 
by them in their collection and employment of the 
data contributed by the several offices. 

The Committee was formed at a Meeting of 
Actuaries, and others connected with Life Assu- 
rance Offices in London, held at the London Coffee- 
House, Ludgate Hill, on Monday the 19th March, 
1 838, at which it was resolved unanimously : 

" That in the opinion of the meeting, it is desirable that the 
different Assurance Offices, should from their records contribute 
the requisite data to the common fund, to afford the means of deter- 
mining the Law of Mortality which prevails among Assured Lives. 

^* That such a Law of Mortality, truly determined, would 
prove generally useful, especially to the Life Offices themselves, 
and the numerous class of persons availing themselves of those 
Institutions. 

*' That persons professionally engaged in similar investigations, 
are most likely to draw correct conclusions from existing data, 
and to classify the same into forms, showing the true rate of 
mortality among Assured Lives." 

The following particulars were obtained from the 
offices that engaged to contribute their experience:— 



For use 

of 
Office. 


Current 
Age at 
Entry. 


Year of 


If by 

Death, 

D. 


Sex, if 

Female 

F. 


Distinc- 
tion into 
Town, T. 


Cause 

of 


Special 
risks and 
Remarks. 


Entry. 


Exit. 


CouutrvC. Death. 
Irish i. 





















D 



Xll INTRODUCTION. 

The following circular^ which was transmitted with 
a supply of forms to each of the contributing offices, 
will explain the particulars that were obtained from 
them : — 

1, King Willimn Street, City, 

2-5tk September, 1838. 
Sir, 

** The Committee of Actuaries desire me, in forwarding the 
accompanying forms, which they have prepared for collecting 
the data, on which to found the experience of Assured Lives 
generally, to submit the following explanation of the nine 
columns into which the forms are divided. 

'^ Column 1. — Headed * For use of Office,' is intended for the 
number of the policy, or any other distinguishing mark, by which 
the person employed to make the extract from the Policy Register, 
may note how far he has proceeded, and be enabled to resume 
the operation without difficulty. 

<* Column 2. — Headed 'Current Age at Entry' is intended 
to contain the age next birth day of the party Assured, at the 
time the Assurance was effected. 

" Column 3. — Headed * Year of Entry' is for the Year in which 
the Assurance was effected. The Committee require neither the 
month, nor the day of the month. The same observation applies 
to column 4, headed ' Year of Exit.' No distinguishing mark 
is required to show whether a Policy has become extinct by 
forfeiture, purchase, or expiration of term; but when extinguished 
by death, a D must be inserted in the next column, No. 5. The 
column marked ^ Exit' will be left blank, opposite all those 
Policies which were in force on the 31st December, 1837, to 
which date it is requested that the list be made up, if convenient. 

" The next column is for distinguishing the sex, in which is to 
be put an F opposite all Policies on the lives of Females ; the 
blanks will indicate Males. Such Offices as have Agents are 
requested to insert a T opposite those Policies effected in Town ; 



INTRODUCTION. Xlii 

a C opposite to those Policies effected in the Country, and an I 
opposite those effected in Ireland, in the column marked * Dis- 
tinction into Town, Country, and Irish.' 

'^ The cause of death is to be inserted in the next column, in 
a line with those Policies extinguished by death. 

" The last column is intended for a notice of special or foreign 
risks, and for the insertion of any observation that may be 
considei'ed useful. 

** The question of founding the experience from returns of 
Policies issued, or on Lives Assured, was fully discussed by the 
Committee, — to confine the returns to a list of the Lives Assured 
in each Office might at first appear desirable, as a means of 
avoiding the insertion of the same Life more than once, in cases 
where more than one Policy has been granted thereon ; but 
when it was considered that in combinino; the returns of several 
Offices, it would be impossible to prevent the repetition of the 
same life, as many are assured in several Offices, and that, in 
combining large numbers where Lives represented by duplicate 
Policies, are subject to the same ratio of mortality as those 
represented by single Policies, the result cannot be sensibly 
affected by the duplication, it was determined by the Committee 
to confine the lists to a record of Policies issued on single Lives." 

I have &c. 

Robert Christie, Hon. Sec. 

From the returns received from the several offices 
in the prescribed form^ and which were blended 
together as they came in, ^^ so as to prevent any use 
being made of the returns separately,"' various 
tables have been prepared, and great care appears 
to have been exercised in the classification of the 
data, upon which the results in the tables have been 
obtained. 



XIV INTRODUCTION. 

The following is a list of the several tables,^ pre- 
pared by the committee. 

Table A (3-6) — Shewing out of the number of Assurances 
effected in each current year of age, the respective numbers in 
each year of duration, cancelled by discontinuance and by death? 
and existing at the termination of the observations. (Separate 
tables for Male and Female lives, Town, Country, and Irish 
respectively.) 

Table B (1-6) — Being an enumeration of entries, existences, 
discontinuances, and deaths, in each year of age, deduced from 
the foregoing tables, A (1-6) (separate tables for Town, Country, 
and Irish Male and Female lives respectively.) 

Table C. — Shewing the number exposed to the risk of mor- 
tality, the actual number of deaths for Assurances on the lives 
of Males and Females, separately and collectively, and for Town, 
Country, and Irish Assurances separately, deduced from Tables 
B and the computed number of deaths, according to the Nor- 
thampton, Carlisle, and Mr. Davies's Equitable Tables of 
mortality, in decennial periods of age, calculated to the nearest 
whole number. 

Table D. (1-5) — Shewing the number exposed to the risk of 
mortality, and the deaths in each year, with the probability of 
surviving one year, and the expectation or average duration of 
life; deduced from Tables B (1-6) (for Town, Country, and 
Irish Male and Female Lives separately, and for Town, Country, 
and Irish experience separately.) 

Table E. — Shewing four times the number exposed to the 
risk of mortality, and four times the number of deaths in each 
year, with the probability of surviving one year, and the ex- 
pectation or average duration of life, deduced from Tables B (1) 
B (4) and other Town experience, which together comprise 
48,702 Assurances. 

Table F. — Shewing four times the number exposed to the risk 

* These Tables are not published, and are only in the possession of the several 
Life Offices who subscribed for copies. 



IlNTRODUCTION. XV 

of mortality, and four times the number of deaths in each year 
with the probability of surviving one year, and the expectation 
or average duration of life; deduced from the total experience, 
which comprises 83,905 Assurances. 

Table G.^ — Adjusted law of mortality, according to the com- 
bined Town and Country experience, deduced from Tables D, 
(4) and E, which comprise 62,537 assurances. 

Equitable experience for separate classes. 

Table H (1) — Shewing results on 7,259 lives admitted between 
the ages of 25 and 35 years. 

Table H (2) — Shewing results on 6,270 lives admitted between 
the ages of 35 and 45 years. 

Table H (3) — Shewing results on 3,436 lives admitted between 
the ages of 45 and 55 years. 

Table H (4)— Shewing results on 1,317 lives admitted between 
the ages of 55 and Q6 years. 

Table I (l)t — Shewing the expectation or average duration of 
life ; deduced from eight original Tables, and compared with the 
Northampton and Carlisle Tables. 

Table I (2) — Shewing the expectation or average duration of 
life, for persons admitted at particular ages in the Equitable 
Society, and compared with Mr. Morgan's and Mr Davies's 
Tables of that Society's total experience. 

Table K. — Shewing the mortality per cent, in each year of 
age; deduced from twelve original Tables. 

Table L, — Shewing the annual number of deaths in quin- 
quennial periods of age, out of 10,000 persons living at each age 
according to various Tables of mortality. 

It appears to have been originally the intention 
of the Committee ''to put the various offices, and those 
who might be interested in carrying out such inves- 
tigations^ in possession of what appeared to be the 
most useful and valuable classifications of the bare 

* See Tables 5, 6, and 7. t See Table 8. 



XVI INTRODUCTION. 

facts comprised in the different returns^ without the 
introduction of any arbitrary or theoretical adjust- 
ments. However^ as some persons might be desirous 
to see an adjusted table of mortality, one has been 
deduced from the combined Town united with the 
Country Assurances^, which comprise the whole of the 
male and female lives that admit of being separated 
from the Irish/^ 

It would have been interesting to have had a 
classification of the causes of death amongst assured 
lives^ but it appears that '' the returns of the causes 
of death were deficient in so many of the lists that 
it was not considered desirable to make any classi- 
fication of them. ^' 

The Author has examined the whole of the Tables 
with great care and with much interest^ but prefers set- 
ting forth the peculiar features exhibited by them in 
the language of the Committee in whose praise too 
much cannot be said for the valuable time and 
trouble which they have gratuitously given to this 
important and interesting subject. 

The Committee state that the most striking 
features exhibited in these Tables^ are the great 
mortality that prevails among Irish lives, and the 
marked difference in the rate of mortality between 
males and females. The near agreement with each 
other of the Tables for " Town '' and " Country " 
Assurances is also very remarkable, considering 
that no adjustment has been employed. 

On comparing the results given in tables C and 



INTRODUCTION. XVU 

L, the mortality annually, taking all ages together, 
is shown to be least amongst '' Town " Assurances, 
rather more amongst ^^ Country/' and greatest 
amongst ^' Irish'" Assurances. The mortality amongst 
assured females, taking all ages together, is also 
greater than amongst assured males ; and both 
these classes exhibit a greater rate of mortality 
than either " Town " or '' Country '' Assurances, 
which arises from the Irish Assurances being in- 
cluded amongst the males and females. 

The mortality represented in table C, is con- 
siderably greater for females than males, between 
the ages of 20 and 50, from 50 to 70 years of age it 
is less, and after the latter age it is at some periods 
rather greater, but the numbers are too small to be 
of any import at these advanced periods of life. 
The ^^ Irish " Assurances are subject to rather less 
mortality under 60 years of age than is represented 
by the Northampton Table ; but after that age the 
mortality amongst them is greater : and taking all 
ages together, the deaths are more than 95 per cent, 
of what might be expected by that table. 

On making a comparison of the different classes 
according to the expectations of life, as shewn in 
Table I, it will be seen that the average duration of 
male lives, under 36 years of age, is greater than 
that of females, and from 36 to 61 years of age, the 
average duration of the lives of females is greater 
than that of males, but after the age of 61, the ex- 
pectation is greater for males than females, which 



Xviii INTRODUCTION. 

may arise from the paucity of numbers at the ad- 
vanced periods of life. The expectation of life for 
the class designated '' Town '' (deduced from the 
facts contained in Table A), will be found to agree 
very nearly with Mr. Morgan's Equitable Table E^ 
being a little more^ but scarcely differing one with 
another a quarter of a year from 22 to 63 years^ after 
the latter age the expectation of life is sometimes a 
little more and sometimes less than by Mr. Morgan's 
Table, but on the whole exhibiting a close agreement. 
The '' Irish '' class gives a considerably less expecta- 
tion of life than Mr. Morgan's Table at all ages ; and 
after the age of 44, the expectation is even less than 
by the Northampton Table. The class designated 
'' Combined Town" in which the " Equitable " and 
^^ Amicable" total experiences are combined with 
the other " Town " Assurances, will be found to give 
the expectation of life rather less than the latter, 
arising doubtlessly from the assurances in the two 
offices just named being of longer duration than 
those in most of the other offices. The expectation 
of life, deduced from the whole of the materials put 
together, it will be seen differs very little from the 
'' Combined Town," The four classes " Town," 
" Country," '' Combined Town," and " General," 
will be found to agree very closely with the ex- 
pectations of life deduced from Mr. Milne's Carlisle 
Table of Mortality, although generally giving a 
lower expectation than that Table." 

In reference to the materials from which the 



INTRODUCTION. xix 

whole of the Tables have been formed^ the Com- 
mittee state that they represent a lower rate of 
mortality than can be expected to prevail in a longer 
period of time than that over which the present 
observations extend ; for the average duration of 
Policies embraced in nearly] one-half of the ex- 
perience is under 5^ years ; and taking the whole 
of the experience together, which includes that of 
the '^ Equitable " and " Amicable, '' the two 
oldest offices existing, the average duration of all 
the Policies is not 8|- years. This is readily ac- 
counted for when it is seen that more than half the 
Policies effected were .existing at the termination 
of the observations, and nearly a 'third had been 
discontinued during the life time of the parties 
assured. The circumstance of recent selection 
should not be lost sight of by such persons as may 
use these Tables either for the sake of comparison 
or as the basis of other tables for granting as- 
surances. The difference in the rate of mortality 
between recently selected lives and those of longer 
continuance in the society is clearly shewn by Mr. 
Galloway in the tables of mortality deduced by him 
from the experience of the '^^ Amicable Society,'^ 
and which that society, like the " Equitable,^' has 
recently so disinterestedly printed for the use of 
its members. ^^ 

It has been thought right to enter thus fully into 
the origin of the publication of the Tables, prepared 
under the superintendence of the Committee o^ 

E 



XX INTRODUCTION. 

Actuaries, and to set forth their opinion of the 
results obtained by them, as it is of the utmost 
importance that the public should be made acquainted 
with the fact that such a committee has been formed, 
and have availed themselves of the most extensive 
and special experience that could be obtained to 
determine the lawof mortality which prevails amongst 
assured lives, and have thus enabled every existing 
office to test the adequacy of its rate of premiums, 
and future offices to provide a rate for themselves on 
a secure basis. 

A rate of mortality having been determined, the 
next important point for consideration is the rate of 
interest which must be assumed, as that which the 
funds invested by a Life Office will realize. Those 
offices which have started at considerably ^^ lower 
premiums than any other office,^^ justify the reduc- 
tion in their rates on the ground of the mortality not 
being so great as that represented by the tables of 
mortality used generally by the offices, and also 
that they can realize a larger per centage on the 
monies invested, than that on which the rates are 
generally based. The mortality deduced from the 
combined experience of the various Life Offices will 
set all speculations at rest as to the rate of mortality 
which may be expected to prevail amongst assured 
lives. With respect to ^^ Interest, "" it will be 
admitted, at least, that it is liable to great fluctua- 
tion, and that money has been for a series of years 
gradually lessening in value. Mr. De Morgan 



INTRODUCTION. Xxi 

observes, in reference to this point, advanced by the 
advocates for low premiums. '^The rate of interest 
has been halved within the memory of man, and a 
heavy war might double it again. That same war 
with all its casualties, direct and indirect included, 
would not alter the mortality of the country by any 
serious amount. I consider it then as next to certain, 
that the insurance offices have more to look for, 
whether as matter of hope or fear, from the fluc- 
tuations of the rate of interest, than from those of 
mortality/' # # # ^ # # 

'^ We are already in a very different position as 
to the rate of interest which has been gradually fall- 
ing since the war. # # # Assuming the neces- 
sity of calculating upon a rate of interest something 
less than that which can actually be attained, I 
should think that no office would be justified in sup- 
posing more than 3 per cent., ivilh tables ivhich are 
sirfficiently high to come any ways near to the actual 
experience of mortality. With regard to one point, 
and that of fundamental importance, namely, the 
possibility of a still further fall in the rate of interest, 
it may even be doubted whether, ivith such tables, 
a still lower rate of interest should not be allowed."' 

But it is urged by the cheap offices, '' Oh, 
but we have a large protecting capital,'" which 
protecting capital, as Mr. De Morgan justly re- 
marks, would, '*^if the premiums were really too 
low, be an injury and not a benefit, for since this 
capital is really paid for in whole or in part out of 



XXll INTRODUCTION. 

premiums^ it would not preserve the office from 
insolvency, but would rather accelerate its progress 
towards bankruptcy/' 

It is needless to observe that proprietors of 
Life Offices do not embark their capital to make 
up an anticipated deficiency, but like other in- 
vestments, their capital is sunk with the view of 
legitimate profit, and as a sqfeguai'd against any 
unexpected or sudden increase in the mortality, and in 
the fluctuation of interest. If they act prudently for 
their own interest, as well as for the safety of the 
assured, they will take care to charge such a rate of 
premium as will, in the opinion of an experienced 
and qualified Actuary, meet every probable risk, and 
cover the expenses of management, and will, in 
addition to the interest to be obtained by ordinary 
investment, also yield them a fair equivalent for the 
money which they have risked for the protection of 
the assured. 

The Author is not contending for high or excessive 
rates ; all that is desired is, that the rates should be 
sufficient and fully adequate to meet the risks and 
expenses incurred. On this point Mr Griffith Davies 
makes the following excellent observations. '' The 
evil of charging excessive premiums cannot, however, 
long remain in a country where capital is allowed to 
flow freely from one channel to another, as the na- 
tural effects of competition must necessarily reduce 
the profits on Life Assurance to the level of that de- 
rived from other species of investments ; on the 



INTRODUCTION. XXlll 



contrary, the peculiar nature of the subject renders 
it extremely dangerous lest the rates for Life Assur- 
ance should be so far reduced as to diminish the 
security of those who may select this mode of ac- 
cumulating their savings for the benefit of their 
families ; for if the premiums charged by societies 
established for these purposes should, by excessive 
competition, be rendered inadequate to the pay- 
ments of the claims which, sooner or later, must 
come upon them, whatever honour, wealth, or pro- 
bity, the present managers of them may possess — 
whatever capitals they may boast of— or however 
prosperous they may appear to go on, even for a 
considerable time, the result must ultimately termi- 
nate in litigation, disappointment and ruin, and in- 
stead of a national benefit. Life Assurance in such 
a case would inevitably become a national calamity.'" 
The Equitable Life Office, whose great success is 
generally appealed to in justification of reduced pre- 
miums, it must be remembered not only enjoyed a 
monopoly, but, as has already been stated, the rate 
of premiums originally charged was enormously 
high, and, in addition to this, they were enabled to 
invest their funds in the purchase of government 
stock at very low prices, for, as observed by the late 
Mr. Morgan, ^^ during the long series of years 
in w^hich this society has existed, the nation, for a 
considerable part of the time, has been engaged 
in foreign wars. These, by depressing public credit, 
have afforded the opportunity of investing money in 



XXIV INTRODUCTION. 

the funds to great advantage^ and have thus contri- 
buted in no inconsiderable degree to create the 
surplus of the society. From the year 1777 to 1786, 
the average price of stock in the 3 per cents, was 
about 60 per cent., and from the year 1796 to 1816, 
the average price of the same stock was below 60 
per cent., or 24 per cent, lower than its present price. 
But no reliance ought to be placed on advantages 
of this kind. Another war may reduce the value of 
stock in the funds to half its present value, or still 
lower, if some of our modern statesmen should 
succeed in breaking the public faith by destroying 
the sinking fund. It would be madness, therefore, 
to found any measure on a property so fluctuating. 
The addition to the surplus arising from the im- 
proved state of public credit is an accidental cir- 
cumstance, affording no proof of the excellence, any 
more than a deficiency in the capital arising from its 
depreciated state would have afforded proof of any 
defects in the construction of the society, and is 
mentioned merely as one of the causes which have 
produced its present opulence/^ 

And in 1828, when the pamphlet from which 
the above observations have been quoted was 
written, and when the price of consols varied from 
82^ to 88|, he proceeds to observe — ^^That all 
the causes hitherto noticed as having conduced 
to promote the welfare of the society, no longer 
exist to enrich it. The premiums have been re- 
duced in some instances nearly one-half. The 



INTRODUCTION. XXV 

policies are seldom or ever forfeited ; and the pur- 
chases made in the public funds at their present 
price are more likely to be disadvantageous than 
beneficial to the society/^ 

From 1829 to the present year the average price 
of consols has been about 90, and the price at present 
is 96^^ so that it will appear that at the present time 
circumstances are peculiarly unfavourable, so far as 
the interest of money is concerned, for the success of 
any new undertaking which does not take the precau- 
tion of adding a considerable per centage to the net 
premiums to cover any extraordinary mortality, 
the expenses of management, and the fluctuation in 
interest. 

By reference to Table 8, it will appear that 
the expectation of an Irish life at 20, is 34.95; 
at 30, 29.71; at 40, 23.36; at 50, 17.76; so that, 
as compared with the combined English experience, 
an office may calculate upon receiving upon an 
Irish life of 20, only thirty-five premiums, instead 
of forty-one; at 30, only thirty instead of thirty- 
five ; at 40 only twenty-four premiums instead of 
twenty-eight ; and at 50 only eighteen premiums 
instead of twenty-one. Notwithstanding this fact, 
in addition to the risk already incurred of charging 
too low a rate of premium even for the English 
lives; if report speaks true, some of the cheap 
offices do a very extensive Irish business, so that an 
extensive business, and the announcements which 

* December 21, 1843. 



XXvi INTRODUCTION. 

are frequently seen among the advertisements of the 
day, to the effect that in addition to a large sub- 
scribed capital, the policy holders have the additional 
security of £ per annum for premiums, are not 
always to be taken as indicative of extensive security; 
for where much Irish business is transacted the ad- 
vertisement, strictly speaking, should run — ^^in addi- 
tion to a large subscribed capital the policy holders 
have the additional security of £ per annum 
annual income for premiums, £ of which are 

from Irish Assurances, from which the society has 
reason to expect they will receive several premiums 
less than they ought, and than which they expect to 
receive on an English Assurance" 

The offices generally are getting very cautious of 
Irish lives, and the circumstance is only mentioned 
here to point out an additional risk that the cheap 
offices incur. 

These remarks have been extended to a much 
greater length than was intended, and the Author 
would, in conclusion, merely express a hope that 
the example of liberality set by the various private 
companies in contributing their experience, and of 
disinterested zeal displayed by the Actuaries who 
superintended the compilation of the materials, and 
deduced therefrom a rate of mortality amongst 
assured lives, will be followed by the government, 
and by their Actuary Mr. Finlaison, in supplying 
the materials which, it is presumed, they possess in 
abundance in several of the government depart- 



INTRODUCTION. XXvii 

ments relative to sickness and mortality, which 
might be worked out by Mr. Finlaison, or under his 
superintendence. In the mean time, it would not, 
perhaps, be considered too liberal on the part of the 
government, if they were to print, for the benefit 
of the public, the various tables on Life Contin- 
gencies, which their actuary has made from govern- 
ment records, and at the national expence, and, 
in reference to which, the following petition was 
printed, and signed by upwards of 40 gentlemen 
connected with Life Assurance Offices in the year 
1837, but which was never presented, probably in 
the expectation that the agitation of the matter 
would be sufficient to induce their publication. 



TO THE HONOURABLE THE COMMONS OF THE 
UNITED KINGDOM OF GREAT BRITAIN 
AND IRELAND, IN PARLIAMENT ASSEM- 
BLED. 

The humble Petition of the undersigned Actuaries of Life 
Assurance Offices, in London, and of others connected 
therewith. 

Sheweth, 

That a very large portion of the property of this country 
is held upon tenures depending upon the duration of human 
life, and that the business of Life Assurance has of late ex- 
tended so as to affect the interests and future happiness of 
large numbers of all classes in the community. 



XXVm INTRODUCTION, 

That one of the principal elements in all calculations of 
the value of property depending on human life, and of the 
value of the risks of Life Assurances, is the average duration 
of human existence, as determined by observations : and the 
means by which such calculations are made or facilitated, 
are tables of the value of Life Annuities, deduced therefrom. 

That as the accuracy of Annuity, and other tables, founded 
on the rate of mortality, depends upon the extent of the 
observations from which they are derived, every addition to 
them is of national importance. 

That to adjust equitably the value of church property, and 
other life interests,— 'to measure truly Life Assurance risks, 
and to afford the means of satisfying the public of the just 
application of correct principles in such valuations, it is 
highly necessary that every authentic information bearing 
upon the subject, should be made generally accessible. 

That very extensive tables, have been calculated at the 
national expense, from data, furnished by Government 
Records, which were printed by order of your Honourable 
House, in 1829 : and that on these tables the Government 
now grant Annuities on lives, and it has recently been pro- 
posed in your Honourable House, that the value of church 
property, should be estimated by the same standard. 

That of these tables a very limited portion only has hitherto 
been made available to the public. 

Your Petitioners, therefore, humbly pray that your 
Honourable House will be pleased to order the pub- 
lication of all tables founded upon the same data as 
those upon which the Government now grant 
Annuities on Lives. These tables will comprehend 
Annuities on Single Lives for males and females 



INTRODUCTION. xxix 

separately, and on every combination of two or 
more joint lives, at every rate of interest at wh ich 
they have been respectively computed. 
London, June^ 1837. 

Joshua Milne, Sun Life Office 

Arthur Alorgan, Equitable Assurance Office 

George Kirkpatrick, Law Life Assurance Office 

Charles Ansell, Atlas Assurance Office 

Griffith Davies, Guardian Office 

J. D. Bayley, Royal Exchange Assurance Office 

Benjamin Gompertz, Alliance Office 

W. S. Lewis, Rock Life Assurance Office 

James J. Downes, Economic Office 

Samuel Ingall, Imperial Life Office 

Robert Christie, Universal Life Office 
Thomas Lewis, Union Assurance Office 

J. M. Rainbow, Crown Assurance Office 

Thomas Galloway, Begistrar, Amicable Society 

E. Charlton, Albion Insurance Office 

"W. Bury, Hope Assurance Office 

H. P. Smith, Eagle Assurance Office 

M. Saward, Promoter Life Office 

Robert John Bunyon, ]S"orwich Union Life Assurance Office 

M. Tate, Pelican Insurance Office 

Edward Hulley, Globe Office 

Henry Marshall, Metropolitan Office 

J. Tullock, Minerva Life Assurance Office 

Charles Jellicoe, Protector Life Office 

John Robertson, Argus Life Office 

Ebenezer Femie, British Commercial Life Office 

J. M. Terry, Hand-in-Hand Life Office 

John Laurence, London Assurance 

G. H. Heppel, Standard of England Office 

J. T. Clement, Licensed Victualler's and General Fire and Life 

Assurance Office. 
Joseph Marsh, Xational Provident Institution 
C. B. Smith, National Life Assurance Society 
Edwin James Farren, Asylum Life Office 
B. A. M. Boyd, Resident Director^ North British Company 



XXX INTRODUCTION. 

J. C. C. Boyd, Secretary J United Kingdom Life Assurance 

J. T. Barber Beaumont, Managing Director, Provident Life 

Office 
Charles M. Willich, Secretary §• Actuary, University Life 

Society 
F. G. Smith, for Scottish Union Assurance Company 
Charles Lewis, West of England Insurance Office 
David Foggo, Secretary, European Life Insurance Office 
T. R. Edmonds, Actuary of Legal and General Life Assurance 

Society 
T. Pinckard, of the Clerical, Medical and General Office 

As the above petition lias never been presented^ it 
has been thought desirable to print it in this Intro- 
duction, as it is important that the public should 
know that there are some valuable and very exten- 
sive tables in the hands of the government calculator, 
which "have been computed at the national ex- 
pence/' and which it is submitted ought to be printed 
for the public information. 



.bvi%>- 



<v 



ur:rv>:RsiTY * 



or 



PRACTICAL EXAMPLES 

ILLUSTRATIVE OF 

THE CONSTRUCTION AND APPLICATION 



OF 



THE TABLES. 



COMPOUND INTEREST, 

TABLE I. 

Interest is a remuneration allowed by a party bor- 
rowing money to the party lending it^ and is payable at 
periods agreed upon at a certain annual rate for every 
£ 1 00. Where it is so paid^ the Interest is called 
'' Simple Interest," but where it is not so paid and 
is added to the sum lent whereby the sum due from 
the borrower is increased by that amount upon which 
(instead of upon the original sum) he will have to 
pay interest— such interest is called ^^ Compound 
Interest." 

EXAMPLE 1. 

What will £450 amount to in 12 years at 4 per 
cent. Compound Interest ? 

If £100 were lent for one year at 4 per cent, its 

B 



amount at the end of the year would be £100 + 4 = 
£104, and this divided by 100 would give the 
amount of £l at the same rate at the end of the year, 
or £1.04 from which we may easily determine the 
amount of any other sum in one or more years ; for 
if 1 : 1.04:: 1.04: (1.04 x 1.04) = 1.04^ =1.0816 the 
amount of £l at 4 per cent, at the end of two years, 
and in like manner; if I : 1.04:: 1.04' : (1.04x 1.04") 
= 1 .04^ = 1.1 24864 — the amount of £ 1 at 4 per cent, in 
three years; and so on for any number of years; the 
amount of £l obtained for any given number of years 
at the given rate of interest multiplied by the amount 
of £l at the same rate for one year will give the amount 
for the succeeding year, and in this manner Table I. 
has been constructed, on reference to which, under 
the head of 4 per cent., against 12 years, we find 
£1,601032 which multiplied by 450 will give 
£720.4644^ = £720 9s. 3Jd., the amount of £450 in 
12 years, at 4 per cent, as required; and so with 
any other amount at the same or any other rate per 
cent. The Rule being — Find the amount of £l in 
the Table under the given rate per cent, against the 
given number of years, and multiply it by the sum of 
which the amount at the same rate and for the same 
period is required. 

If the interest is payable half yearly the rule is — 

* To persons unacquainted with Decimals, it would be useless to 
give a rule for the conversion of shillings, pence, and farthings into 
decimals, and vice versa, such persons, therefore, are referred to works 
on Arithmetic. To those who are acquainted with Decimals it is 
unnecessary to do so. 



Take one half of the annual interest and double the 
number of years, and proceed as iV* the case where 
interest is paid annually. For example^ if in the 
above case the interest were payable half yearly, the 
amount would be obtained thus — Under column 
2 per cent., in Table 1, and against 24 years, we 
find £1.608437 — the amount of £l at 2 per cent, 
per annum in 24 years, or, which is the same thing, 
the amount of £l at 2 per cent, per half year in 
24 half years, which, multiplied by 450, gives 
£723.79665 =£723 15s. lid.— Answer. And if 
interest were payable quarterly the rule would be — 
Take one fourth of the annual interest and multiply 
the number of years by 4, and proceed as in the case 
where interest is paid annually. If, in the above 
example, the interest were paid quarterly, we should 
refer to column headed 1 per cent., in Table 1, and 
against 48 years, we should find £1.612227 the 
amount of £l at 1 per cent, per annum in 48 
years; or, which is the same thing, the amount 
of £l at 1 per cent, per quarter, for 48 quarters 
of a year, which, multiplied by 450, would giw^ 
£725.50215 = £725 10s. 0|d.— Answer. 

It evidently matters not whether the ^' rate" be 
called the rate per annum, or per half year, or per 
quarter, as the amount of any sum at a given rate of 
interest manifestly depends upon the number of 
conversions of interest into principal. 

EXAMPLE 2. 

The amount of £450 in 12 years at 4 per cent., 



Compound Interest, payable 

annually, - - being £720 9s. 3^d. 

n payable half yearly // £723 15s. lid. 

// // quarterly // £725 lOs OW. 

it is required to find the total amount of interest 
realized. This will evidently be the difference be- 
tween the sum lent and its amount at the end of 
the time, and will be respectively, 
£720 9s. 3|d.— £450 = £270 9s. 3|d., Amount of 

interest realised upon £450 in 12 years, at 4 per cent, interest, payable yearly. 

£723 i5s. 11 d.— £450 = £273 15s. lid., do. do. pay- 

able half-yearly. 

£725 10s. 0|d.— £450 = £275 10s. 0|d, do. do. pay- 

able quarterly^ 



DEFERRED SUMS CERTAIN. 

TABLE II. 

The present value of a sum of money to be received 
at the end of any number of years, is that which, 
laid out at a given rate per cent, will amount at 
that rate, to the sum to be received at the expiration 
of the given period. 

EXAMPLE. 

In exmaple J, of Compound Interest £720 9s. 3Jd. 
= £720.4644 is stated to be the amount of £450 at 4 
per cent, in 12 years. £450, therefore, ought to be 
shewn by Table 2, to be the present value of 
£720 9s. 3^d. to be received at the expiration of 12 
years, supposing interest to be 4 per cent. 

On referring to Table 2, under the head 4 per 



cent., and against 12 years, will be found £".624597, 
the present value of £'1 to be received at the expi- 
ration of 12 years, which multiplied by 720.4644 
will give £450, the present value required. This 
sum might have been obtained by dividing£720.4644 
by 1.601032 the amount of £l in 12 vears. For 
if 1.04 ; 1 :: 1 : r^j the present value of £l at 4 per 
cent. Compound Interest to be received at the ex- 
piration of one year; and similarly, — if 1.04 : 1 :: 
i^ : i:^ — present value of £l at the same rate to be 
received at the expiration of two years : and so on 
for any number of years. In this manner Table 2 
has been formed — ujiity being divided by the amount 
against each age at the several rates per cent, in 
Table 1 ; and it is manifest that when the present 
value of £l for any number of years at a given rate 
is found, that the Rule for finding the present value 
of any other sum at any rate per cent, will be Mul- 
tiply the present value of £\ at the given rate and the 
given number of years by any other amount of which at 
that rate and for that teryn the present value is re- 
quired. 



ANNUITIES CERTAIN— AMOUNTS. 

TABLE III. 

An Annuity Certain, is a sum of money pavable 
at fixed periods without being subject to anv contin- 
gency. 



6 



EXAMPLE. 

What will an Annuity of ^20 per annum amount 
to in five years, at 6 per cent. Compound Interest ? 

On reference to Table 3_, under 6 per cent, against 
5 years will be found 5.637093, the amount of an 
Annuity of .^'l at that rate and for that term, (or, as 
it is usually called, the number of years purchase,) 
which multiplied by 20 gives £'112,74 1 86 =.£^112 
14s. lOd. — Answer. 

The results contained in the Table were obtained 
thus : — 
The last payment of an Annuity of £l, at 6 

per cent, and upon which no Interest is 

received is £1.000000 

The last payment but one, and upon which 

one year's Interest accrued 1.060000 

Their Sum — Amount of Annuity in 2 years 2.060000 
The last payment but two, with 2 years' 

interest 1.123600 

Their Sum — Amount of Annuity in 3 years 3, 183600 
The last payment but three, with 3 years' 

Interest 1.191016 

Their Sum — Amount of Annuity in 4years 4.374616 
The last payment but four, with 4 years' 

Interest 1.262477 

Their Sum £5.637093 

amount of Annuity of £l forborne 5 years (or the 
number of years purchase) and agrees with the 



amount given above as taken from the Table ; and 
by proceeding in this manner the Amount of an An- 
nuity for any rate and for any period may be obtained. 
The Rule for the construction of the Table being 
To £l .00000, add the amount of £l at the expiration 
of one year, at the ^iven rate of interest obtained from 
Table 1, which will give the amount of an anjiuity at 
that rate forborne two years, to this sum add the 
amount of £l in two years, which will give the 
amount of the aimuity for three years, and so on (as in 
the above example) to the end of the period required. 
The Table being formed, the rule for finding the 
amount of any other sum annually will he,Obtainfrom 
Table 3 the Amount of an Annuity of£\ at the^iven 
rate per cent, and for the given tenn, ajid multiply it 
by the annuity, whose amount, at the same rate and for 
the same period is required. 

If the annuity is payable half yearly, Take the 
quantity from the Table under half of the rate per 
cent, opposite twice the number of years, and multiply 
it by one- half of the annuity. 

If payable quarterly, Take the quantity opposite 
one-fourth the rate per cent, and opposite four times 
the number of years, and multiply it by one-fourth of 
the annuity. 

Or the amount of an Annuity might be found by 
the following Rule : — 

Obtain from Table 1 the amount of £ I at the given 
rate of Literest and against the given nmnber of 
years ; subtract unity from it and divide the remainder 
by the Interest of £{ for one year at the same rate. 



8 

which will give the mnourit of an Annuity of £\ at 
that rate and for that term, and multiply the quotient 
by the Annuity ivhose amount is required Table 3 
might also have been formed in this manner though 
not so readily. 

The reason of this rule is manifest, for when unity 
is deducted from the amount of ^£"1 at the given 
rate and for the given term obtained from Table \, 
the remainder must be the total amount of interest 
realised, and this amount accrued by putting by the 
interest due each year, upon which also interest was 
obtained, therefore the diiference between the 
amount of ^1, at any rate and for any term, and £\, 
the sum originally laid out^ is equal to the amount 
of an annuity of the interest of £l B,t the same rate 
and for the same term. 

The above example might therefore have been 
obtained thus. From the amount of ^£"1 at 6 per cent, 
in five years, which, by Table 1, is ^1.338226, take 
£\, the original sum laid out, and the difierence 
<£0.338226 is the total interest realised, or the amount 
of an annuity of £.06 at 6 per cent, in five years ; 
then, by the common rule of proportion : — If 
^.06 : £0 338226 ::£'l : .56371 -the quantity, given 
above as obtained from Table 3, to the nearest 4th 
place of decimals, which, multiplied by 20, gives 
^112.742=^112 14s.l0d. as before. 

Table 3, has been constructed upon the suppo- 
sition that the annuity is payable at the end of the 
year ; if it were payable at the beginning of the year 
each of the amounts in that Table ought to be in- 



9 

creased by one year's interest ; the amount of the last 
payment, therefore, reckoning interest at 6 per cent, 
upon which one year's interest accrued 

would be =£^1.060000 

The last but one upon which two years 

interest had been received 1.123600 

Their sum f 2.183600 

the amount of an annuity payable at the beginning 
of the year, laid by for two years, which is equal to 
the amount of an annuity payable at the end of the 
year for three years less unity ; so that where the 
annuity is payable at the hegirming of the year, the 
rule is Subtract unity from the amount of an annuity 
payable at the end oj the year — in Table 3 — at the 
given rale of interest opposite one year more than the 
time. 



ANNUITIES CERTAIN— PRESENT VALUES. 

TABLE IV. 

1st. Immediate Annuities. — The present value 

of an Annuity to be entered upon immediately and 

to continue for a term of years, is that sum 

which paid down now and invested at a given rate 

of Interest will, at the expiration of the term, 

c 



10 

amount to the same sum as will the Annuity itself 
invested in like manner. 

EXAMPLE 1. 

What is the present value of an Annuity of .^'SO 
per annum to continue 4 years^ reckoning Interest 
at 4 per cent.? 

On referring to Table 4^ under the head of 4 per 
cent, and opposite to 4 years will be found .^'S. 629895 
the present value of an Annuity of £} at that rate 
and for that term, which multiplied by 30, gives 
£'108.89685=^108 18s.— Answer. 

Proof. — By Table 1, under the head of 4 per cent, 
and against 4 years we find ,£'1.169859^ the amount 
of c^'l in 4 years at 4 per cent.^ which multiplied by 
1 08.89685 =<£'127. 3938 =£127 7s. lOd., the sum 
to which £108.89685 the present value of an An- 
nuity of £30 at 4 per cent, will amount to in 4 
years^ and 

By Table 3, under 4 per cent, and against 4 years 
will be found £4.246464, the amount of an Annuity 
of £l in 4 years at 4 per cent.^ which multiplied by 
30 =£127.3939 = £127 7s. lOd. the amount of an 
Annuity of £30 at the same rate and for the same 
term^ thus proving the accuracy of the present value 
as determined from Table 4. 

The total present value of an Annuity for a term 
of years is manifestly equal to the sum of the present 
values of each yearns payment^ and by the continued 
addition of these at the several rates of Interest 
Table 4 has been formed. For example — by Table 2. 



11 

.£0.961538 is given as the present value of .^l to be 
received at the expiration of 1 year at 4 
per cent. Interest. 

£0.924556 ditto ditto at the expiration of 2 years. 

£1.886094 Sum of the above^ or present value of an 
Annuity of £\ for 2 years. 

£0.888996 present value of£l to be received at the 
expiration of 3 years. 

£2.775090 Sum of the above, or present value of an 
Annuity of £l for 3 years. 

£0.854804 present value of £l to be received at the 
expiration of 4 years 

£3^629894 Sum of the above^ or present value of an 
Annuity of £l for 4 years^ &c. &c. 

2nd. Perpetual Annuities. — The present value 
of a Perpetual Annuity is that sum which paid now 
and invested at a given rate of Interest will per- 
petually produce the same amount as will the An- 
nuity itself invested in like manner. 

It is manifest that if £100 were sunk at 5 per 
cent, that it would be the present value of a Perpe- 
tual Annuity of £5^ and consequently that £20 would 
be the present value of a Perpetual Annuity of £l^ 
for— If £ 5 : 100 :: 1 : 20 or 

If £.05 : £1 :: 1 : 1^= 20— and 
in a similar manner the present value of a perpetuity 
at any other rate of Interest might be found^ there- 



12 

fore The present value of a perpetuity of £\ may he 
found by dividing £l by the Interest of £\ at the 
given rate for one year, and the quotient multiplied 
hy any other perpetuity will give the present value of 
such perpetuity, 

EXAMPLE 2. 

What is the present value of a Freehold Estate 
producing £l50,per annum^ reckoning Interest at 
4 per cent.? 

At the end of Table 4^ under column headed 4 per 
cent, will be found 25 =;^^ which multiplied by £150 
= £3750. — Answer. 

Now at 4 per cent. £3,750 sunk will yield .£150 
per annum, therefore £3,750 invested at 4 per cent, 
and never withdrawn, is equal to a Perpetual An- 
nuity of £150 invested in like manner, it producing 
annually exactly that sum. 

3rd. Deferred Annuities. — The present value 
of an Annuity not to be entered upon until the expi- 
ration of a given period, is that sum which paid down 
now and invested at a given rate of Interest will, at 
the end of the period during which the Annuity is 
deferred, amount to the sum which will then^ at the 
same rate of Interest, purchase the Annuity in ques- 
tion to be entered upon immediately, 

EXAMPLE 3. 

What is the present value of an Annuity of £30, 
to be entered upon at the expiration of 4 years and 
then to continue 10 years, reckoning Interest at 4 
per cent.? 



13 

By the exemplification of the construction of 
Table 4, it has been shewn that the total value of an 
annuity for any given term is equal to the total ot 
the present values of each year's payment through- 
out the term, consequently if the present value of 
the firsts or any number of year's annuity, is deducted 
from the present value of the annuity for the whole 
term, the difference will be the present value of the 
annuity for the remainder of the term. 

In the present case 4 + 10 = 14 — the period during 
which the annuity is deferred, added to the period it 
is to be continued when entered upon, and on re- 
ference to Table 4, under 4 per cent., and against 
14 years, will be found 10.563123, the present value 
of an annuity of ^1, to be entered upon immediately, 
and to continue 14 years, and in the same column 
opposite 4 years will be found £"3.629895, the present 
value of an annuity of fl, to be entered upon imme- 
diately, and to continue four years, therefore 
^10.563123— £3. 629895 =f6.933228,present value 
of an annuity of £\, to be entered upon at the ex- 
piration of four years, and then to continue ten years, 
which, multiplied by30 = £207,99684 = £207 1 9s. 1 1 d. 
the present value of an annuity of £"30 deferred for 
the like period and to be continued for the same term. 

Proof. — On reference to Table 1, under the head 
of 4 per cent., and against four years, will be found 
£"1.169859, the amount of £l in four years, at 4 per 
cent. which,multiplied by 207. 99684 gives£243. 3268, 
which will be found to be the present value of an 
annuity of £30, to be entered upon immediately, and 



14 

to continue ten years ; for, by Table 4, under 4 per 
cent, and against ten years, we find £^. 1 10(396^ the 
present value of an annuity of.^"!^ to be entered upon 
immediately, and to continue ten years, which, multi- 
plied by 30, will give ^243.3268, as before. 

If the annuity were a Deferred Perpetuity, the 
present value would be found in a similar manner ; 
the general rule being, From the present value of the 
annuity for the whole of the term, at the given rate 
of interest, subtract the present value of the ajinuity 
at the same rate for the term during ivhich it is to he 
defeiTed. And, consequently, the value of a deferred 
annuity subtracted from the value of the whole term 
annuity, will leave the value of the temporary an- 
nuity, i. e, of the annuity for the term deferred. 



NEW RATE OF MORTALITY. 

TABLE V. 

The numbers in column 2, of Table 5, against each 
age in column 1 are the numbers which have com- 
pleted or survived those ages out of the 100,000 who 
completed their 10th year of age, and from which, 
by the simple rule of Proportion, the number who 
might be expected to survive any given age or die 
within the term, out of any other number, at any 
age, &;C. may be ascertained. 



15 

EXAMPLE 1. 

Out of 3,500 persons living at the age of 20, how 
many may be expected to survive the age of 40 ? 

On reference to Table 5, it will be found that 
there are at 20 years of age 93/268 persons living, 
of whom 78.653 survive the age of 40; then 

As 93.268 : 78,653:: 3500 : 2952 /zmr/j/, tlie num- 
ber out of 3500 at the age of 20 who may be ex- 
pected to survive the age of 40. 

EXAMPLE 2, 

It is required to determine the number of deaths 
that may be expected out of 3500 persons alive at 
the age of 20 during the next 20 years ? 

By Table 5, it appears that the number living at 
the age of 20 is 93,268 and the number livino- at the 
age of 40 is 78,653, therefore 93.268 — 78.653 = 
14.615 the number who died during the interval, 
hence 93,268 : 14.615 :: 3500 : 549 the number who 
may be expected to die in 20 years or before attain- 
ing 40 years of age, out of 3500 alive at 20 years of 
age. 



PROBABILITIES OF LIFE. 

TABLE VI. 
EXAMPLE 1. 

Required, the probability of a person aged 30, 
dying within and surviving one year ? 



16 

On reference to column 2^ in Table 6, and against 
30 years of age, will be found .0084248, the proba- 
bility of a person aged 30 dying in one year ; and 
on reference to column 3, in the same Table and 
against the same age, will be found .9915752, the 
probability of a person aged 30 surviving one year ; 
and the two added together will give unity or cer- 
tainty, for it is manifestly certain that a person at 
any age will either survive a given period or die 
within it, from which it follows that if we know the 
probability of a person at any age dying within any 
given period, and subtract it from unity, the dif- 
ference or remainder will be the contrary proba- 
bility, or the probability of surviving the given 
period ; and, on the other hand, if we subtract the 
probability of surviving from unity , the remainder 
will give the probability of not surviving, or of dying 
within the given period. 

The probabilities of dying within one year are 
obtained by dividing the number of deaths against 
each age by the number living at the same age, and 
the quotient subtracted from unity gives the pro- 
bability of surviving one year. Or, the probability 
of surviving one year may be obtained by dividing 
the number living one year older than the given 
age by the number living at the given age, and the 
quotient subtracted from unity gives the probability 
of dying within one year. And in this manner Table 
6 was constructed. 



17 

EXAMPLE 2. 

Required the probability of a person aged 16, sur- 
viving the age of 20 ? 

This will evidently be the number living at the age 
of 20, divided by the number living at the age of 
16, or by Table 5, |?|- = .97190 

EXAMPLE 3. 

Required the probability of a person aged 16, 
dying in the 21st year of his age. 

The number who die in the 21st year of age, 
being the decrement set against age 20, according 
to Table 6, is 680, and this divided by 95965, 
the number living at 16, will evidently give the 
probability of one of that number dying in the 21st 
year of age, or J-^; this probability might have 
been obtained by subtracting the probability of the 
life surviving the 21st year of age, from the proba- 
bility of its entering upon that age, or the probability 
of its surviving the 20th year of age, thus : — 

.Q3268 92588 680 ' . . . 

— . — — — = as beiore, and 

95965 95965 95965 ' 

this will be manifest upon inspection, as the first 
numerator is the number living at 20, and the 
second, the number living at 21, and the difference 
is the number of deaths which occur within the 21st 
year, and the denominator the number living at 16, 
is common to each of the three fractions. 

From the above it will appear that, the rule for 

D 



18 

determining the probability of a life surviving any 
age is. 

Divide the number living at the advanced age by 
the number living at the present age. 
And of its failing in any year of age, 
Divide the number of deaths tvhich occur in that 
year"^ by the Jiumher living at the present age; or sub- 
tract the probability of the life surviving the given 
year from the probability of its entering upon that year. 

EXAMPLE 4. 

Suppose a Life Assurance Office to have 2000 
policies in force, averaging £1000 each policy, viz., 
200 at 25 years of age ; 300 at 30 ; 400 at 35 ; 500 
at 40 ; 300 at 45 ; 200 at 50 ; 50 at 55 ; and 50 at 
60 ; it is required to determine the number and the 
amount of claims by deaths that may be expected to 
be made within one year. 

The probabilities of surviving and of dying in 
Table 6, being the probabilities of one person at the 
given ages dying within, or surviving one year, it is 
manifest that the probabilities of any other number 
dying within, or surviving that period, will be 
obtained by multiplying such probabilities by the 
number in question. Hence, 

Probability of one Number Probable 

Age. Person dying in of number of 

one year. Persons. Deaths. 

25 .0077700 x 200 = 1.55400 
30 .0084248 x 300 = 2.52744 



* The number of deaths which occur in any year is represented by the decre- 
ment set opposite the next younger age. 



19 



Age. 


Probability of one 

Person dying in 

one year. 


Number 
of 

Persons. 


Probable 

number of 

Deaths. 


35 


.0092877 X 


400 = 


3.71508 


40 


.0103619 X 


500 = 


5.18095 


45 


.0122120 X 


300 = 


3.66360 


50 


.0159386 X 


200 = 


3:18772 


55 


.0216643 X 


50 = 


1.08321 


60 


.0303362 X 50 = 
I number of Deaths that may 


1.51681 


Tota] 




be 


expected. 


. 


22.42881=22^ 



nearly, which multiplied by £1000, the amount of 
each policy, gives ^£^22,429, the whole amount of 
claims that may be expected. This number, and the 
amount being determined from the policies in force 
at the beginning of the year, only indicates the 
probable number and amount of claims that may be 
expected to arise out of that number only, and 
upon the supposition that all the policies continue in 
force, except those which become claims. But as 
an addition will be made during the year, by the 
introduction of new business, and as some policies 
may lapse, or be surrendered, they must be taken 
into account before a comparison can be made of the 
number of deaths that might be expected, with the 
number that actually occurred. Of the new policies, 
and those surrendered, it may be assumed that taking 
one with another, they were each in force one half- 
year, or, which is the same thing, that one-half of 
them were in force the whole of the year. In 
making tlie comparison at the end of the year, there- 



20 

fore, one-half of tlie number of neiv policies at 
each age, should be added to the number in force 
at each age at the beginning of the year, and one-half 
of those lapsed or surrendered at each age should 
be deducted from the number in force at each age, 
the numbers being thus corrected, the number of 
deaths expected according to the Table may be 
obtained as above. An office may, therefore, with 
very little difficulty, ascertain whether the amount 
of claims during the year is more or less than they 
had reason to expect. 

EXAMPLE 5. 

Required the probability of two lives aged 16 and 
21, both surviving 5 years ? 

The probability of a life aged 16, surviving 5 years,, 
by Table 5 is ^; and of a life aged 21, surviving 5 
years, is ^^; and these two quantities multiplied to- 
gether will give the probability in question. For 
unity or certainty bears the same ratio to either of 
the probabilities as the remaining probability does 
to that required, viz., 

^g . 92588 .. 89137 . 92588 ^ 89137 
* 95965 " 92588 * 95965 92588 

= ^^^^^ = .92885 Answer. 
95965 

Then to find the probability of any two given 
lives, both surviving a given period, the rule is simply, 



21 

3Iulliphj the separate probabilities together, and 
the product will be the probability/ required ; and the 
same rule applies to the probability of any two lives, 
both failing in, or within any given period, and in a 
similar manner the probabilities of three or more 
lives surviving, or failing within a given period, 
may be obtained. 



EXPECTATION OF LIFE. 

TABLE VII. 

By Expectation of Life is meant the average 
number of years that a person, at any age, may yet 
expect to live, taking one life with another. For 
example, a person aged 30, (see Table 7, 30 years 
of age,) according to the experience amongst 
assured lives many expect to live 34J years nearly, 
or, in other words, he may expect to attain the age 
of 64|- years nearly. 

The total-existence enjoyed in any one year by the 
number of persons alive at any age at the expiration 
of one year, will manifestly be as many years as there 
are persons who survive the year, added to the 
existence enjoyed by those who die within the year. 
And of those who die within the year, it is probable 
that as many die at equal intervals during the first 
half year, as die at the same intervals during the 
last half of the year, or, in other words, that of 



22 

those who die in any one year, taking one life with 
another, it may fairly be assumed that, upon an 
average, they each enjoy one-half year's existence — 
therefore, the total existence enjoyed at the expira- 
tion of a year, by those alive at any given age at 
the beginning of the year, is equal in years to the 
number who survive the year, plus one-half of those 
who died within the year. 

EXAMPLE. 



Required the number of years that a person aged 
90, may expect to live. 



On reference to Table 5, i( 
that, of 13] 9 persons alive at 
of 90. 


appears 
the age 


Who enjoyed between 
them in each year as 
many years as there are 
persons, or the under- 
mentioned number of 
years. 


To which we 
must add one- 
half of the num- 
ber who died in 
each year or 


Which 

gives. 


892 survived 1 


year. 


892 


2134 


I105i 


570 „ 2 


^» 


570 


161 


731 


339 „ 3 


>) 


339 


115i 


454* 


184 „ 4 


?y 


184 


774 


2614 


89 „ 5 


}? 


89 


474 


136* 


37 „ 6 


yy 


37 


26 


63 


13 „ 7 


yy 


13 


12 


25 


4 „ 8 
1 „ 9 
„ 10 


yy 
yy 


4 
1 




H 
1 

2 


n 
1 

2 



Sum = 



^-2788* 



2129 + 659| 
And this divided by 1319, gives 2.11, or % years 
expectation of life to a person aged 90, and agrees 
with the expectation as given in Table 7, opposite to 
90 years of age. 

The 659*, the sum of all the halves of the number 



23 

of deaths in each year, is manifestly one-half of the 
number who were alive at the age of 90 ; the expec- 
tation might, therefore, have been obtained by 
dividing the sum of all who survived that age 2129, 
by the number alive at that age 1139, and adding to 
the quotient ^ for 

27S8i _ 2129 + 6591- _ 2129 ^ i 



1319 1319 1319 



+ i = 2.11 



so that a Table of the Expectations of Life may 
easily be formed, by first obtaining the successive 
sums of the numbers surviving each age. and then 
dividing them by the number living at each age, and 
adding ^ to the quotient, and in this manner Table 
7 was constructed. 



COMPARATIVE EXPECTATIONS OF LIFE. 

TABLE VIII. 

This Table speaks for itself, and sets forth the 
Expectations of Life as deduced from various rates 
of mortality, and also amongst the different descrip- 
tions of assured lives, and will be found not only 
very interesting, but very important, particularly 
as from the Irish experience, it appears that, of that 
class of assurances, at some of the younger ages, the 
Expectation of Life is as much as 6 years less than 
that obtained from the combined English town and 



24 

country experience. — (See observations on the Irish 
experience, in ^' Introduction/'') 



LIFE ANNUITIES AND ASSURANCES. 
TABLES IX. X. AND XI, 

ANNUITIES. 

Required the Value of an Annuity of £l per 
annum, on a life aged 97, reckoning interest at 3 per 
cent ? 

If this were an annuity certain, its value 
would be equal to the sum of the present values of 
^1, to be received at the expiration of 1 and 2 years, 
but as the payment of the annuity is contingent upon 
the existence of the life the value of each year's pay- 
ment of the Life Annuity will be less than that of an 
annuity certain^ in the ratio oi unity or certainty to 
the probability of the life surviving each year. 

By Table 2, under the head of 3 per cent., we 
find. 

.970874 = present value of £\y to be received at 
the expiration of one year. 

.942596 = ditto ditto, two years, 
and, by Table 5 we find the number living at the ages 
98 and 99 to be respectively 4 and 1, and these, 
divided by 13, the number living at 97 will give -^ 
and ^, the probability of a life aged 97 surviving 98 



25 

and 99 years of age; the latter — the oldest age 
which can be survived according to the Table. The 
present value of the first year's payment^ therefore, 
on a life aged 97, will be 

As 1 : -i :: .970874 = i-^-^^^ 

And of the second, 

As 1 : 7^ :: .942596 = — 

And the total value will be 

( 4 X 970874) + 1 x (.942596 ) __ 4.826092 

13 "" 13 =^•^'^1 

as given in Table 12, in column headed 3 per Cent., 
opposite to 97 years of age. 

Now the value of a fraction is not altered in any 
degree by multiplying its numerator by any quantity 
provided Y^e also multiply its denominator by the same 
quantity. For example, if we multiply the numera- 
tor and denominator of the fraction ^, by 2 and by 
30, we get \, and ^-g, each of which is still equivalent 
to ^, for if the fraction in question be of 
60 shillings, ^ of it is 30s., and ^ of it being 
15s., ^ths. is necessarily 30s., and, in like manner^ 
^th. of 60s. being Is., the |J ths. must be 30s. and 
so with any other fraction. If, for example, we say, 
the probability of a person living 1 year is |^, of 
another ?, and of a third g^ths, their probabilities 
are each equal to |^, this being premised, what follows 
will appear clear. 

The following are the quantities given above, from 

D 



20. 

which the value of an annuity, on a life aged 97, at 

3 per cent, interest, was obtained . 

(4 X .970874) + (1 x .942"596) _ 

J3 -0.371 

which, expressed in words, is the number living at 
98 years of age, multiplied by the present value of 
£l, to be received at the expiration of 1 year,^Zws 
the number living at the age of 99, multiplied by the 
present value of ^1, to be received at the expiration 
of 2 years, divided by the number living at the age 
of 97. 

Now, if we multiply each of the quantities in the 

numerator and denominator by .056858 the present 

value of <£l, to be received at the expiration of 97 

years, (the same as the age of the life,) we shall get 

(4 X .055202) + (1 X .053594) 

13 X .056858 

i e. the number living at 98, multiplied by the pre- 
sent value of ^1, to be received at the expiration of 
98 years, plus the number living at 99, multiplied by 
the present value of .f'l to be received at the expira- 
tion of 99 years, divided by the number living at 
97, multiplied by the present value of ^1, to be 
received at the expiration of 97 years, which is 
equal to 

:^^ = .37. as before, 

and in a similar manner, the value of an annuity 

at any other age may be obtained. 

![_ But the D and N columns for the rates 2|^, 3, and 



•27 

3 J per cent, in Tables 9, 10, and II, contain the 
numerator and denominator that will obtain at each 
age ; the quantities in column D being the number 
living at each age, multiplied by the present 
value of £l, to be received at the expiration 
of as many years as the age, and the quantities in 
column N, opposite to each age, are respectively 
the sum of all the quantities in column D., at all the 
ages older than the given age; therefore, 

T/ie quantity in column N, opposite to any age, 
divided by the quantity in column J), at the same age, 
will give the value of an annuity at that age. 

And in this manner the values of the annuities at 
2^ 3, and 3h per cent, in Table 12 were obtained. 

For example, at 2|- per cent. (See Table 9.) 

Nat 98 = 00^676 ^ .^44 the value 
D at 98 = 0.35573 

of an annuity of £l per annum on a life aged 98, 
and agrees with the value given in Table 12. 

N at 97 = 0^44249 ^ 3^3 ^^^ ^^^^^ 
D at97 = 1.18503 
of an annuity of £\ per annum, on a life aged 97, 
as also given in Table 12- 

Column S in Tables 9, 10, and 11, is the sum of 
the quantity at each age, and at all the ages older 
than the given age in column N, and is useful in find- 
ing the values of increasing and decreasing annuities. 

ASSURANCES. 
The diiference between the value of an Annuity 



28 

and that of an Assurance is, that in the former, as has 
already been shewn, each yearns payment depends 
upon the probability of the life surviving each year 
of age, whereas, in the latter, the value depends 
upon the probability of the Mi^ failing in each year, 
and in the calculation of the premiums, the sum 
assured is, in all cases, assumed to be payable at the 
expiration of the year in which the life fails. 

The present Value, therefore, or ^' Single Pre- 
mium '' for an assurance on a life at any age, is equal 
to the sum of the present values of <£l certain, to be 
received at the expiration of 1, 2,3, &c., &c. years to 
the end of life, multiplied respectively by the proba- 
bility of the life failing in each year. 

EXAMPLE. 

Required, the single premium to secure £\ on a 
life aged 97, reckoning interest at 3 per cent. 

By Table 2,— .970874 = Present value of £l to be 

received at the expira- 
tion of 1 year. 
„ .942596 = ditto ditto, 2 years 

„ .915142 = ditto ditto, 3 „ 

And by Table 5, — — = Probability of a life aged 97 

failing in or before comple- 
ting the 98th year of age. 
^ = ditto 99th year. 



1= ditto 100th ditto. 



Then, 



13 



( 9 X .970874 ) + (3 x .942596) + (1 x .915142) ^^ 

yn ^ = .96005 



29 

the Single Premium required ; but if^ as in the case of 
Annuities (see page 26) we multiply the numerator and 
denominator by .056858 the present value of ^'l to 
be received at the expiration of 97 years, (the same 
number of years as the age,) the value will not be 
altered, and we shall have 
( 9 X .055202) + (3 X .053594) + (1 x .052033) 

1 3 X. 056858 -.Jb005 

as before, and in a similar manner the single pre- 
mium for an assurance at any other age may be found. 
But we have already got each of the denominators 
that would obtain at each age (the number 
living at each age multiplied by the present value 
of ^1, to be received at the expiration of the 
same number of years as the age) — in column D, 
and the quantity in column M, opposite to any age, 
is equal to the sum of the decrements opposite to 
that age, and all the ages older than the given 
age in Table 5, multiplied respectively by the present 
value oi £\. to be received at the expiration of one 
year more than the given age, as, for example : 

Present value 

Deere- ""^ ^^ ^"^,** 
^Se- ment the end of one 
year more than 

the age. 

99 1 X .052033 = .052033 =M, opposite to 99 years 

of age 
98 3 X .053594 = .160782 

Sum = .212815 = M, ditto, 98 
97 9 X. 055202 = .4968 18 

Sum = .709633 =M, at 97 

and the last quantity, .709633, is the sum of the pro- 
ducts in the numerator above, and agrees with the 



30 

quantity in Table 10, in column M, opposite to 97 
years of age^ and the quantity in column D^ opposite 
to 97 is .73915^ and corresponds with the pro- 
duct of the quantities in the above denominator. 

Then —^ =.96005 as before, and agrees with 
the quantity in Table 15^ in column headed^ 
^^ Single Premium^'^ opposite to 97 years of age, 
so that, where the columns D and M, are formed 
the rule to determine the single premium is. 
Divide the quantity in column M opposite to the age 
hy the quantity in column D, opposite to the same age. 
and, in this manner, the single premiums at each 
asre in Table 15 were obtained. 

If the annual premium for an Assurance were £l 
per annum, its equivalent present value, or ^^ Single 
Premium," would manifestly be £l paid down,^ 
added to the present value of an annuity of £*!, to be 
paid during the life in question, or on a life aged 97 
.27439 =N, opposite to 97 
"^ .73915 = D, do. 

,.,. ,, .73915 + .27439 1.01354 

which IS equal to ^g^^^ = -j^gy^ 

then by the simple rule of proportion. If 

1.01354 , .70962 = M, at97 .70962 .73915 



.73915' .73915 =D, at 97 • .73915 1.01354 

.70962 = M, at 97 „^^. . 

= . . XT ^ n/? .70014 

1.01354 =N, at 96 
the annual premium for an assurance of jf'l on a life 
aged 97, and corresponds with the quantity given in 

* The Annual Premium for an assurance is always paid at the beginning of the 
year. 



31 

Table 15, in column headed ^^ Annual Premium/' 
opposite to 97 years of age. 

The rule^ therefore, to determine the annual pre- 
mium for an assurance of £^1 is, 

D ivide I he quantity in cohuim M, opposite to the given 
age, hy tJie quantity in column iV, opposite to the age 
one year younger; and, in this manner, tlie annual 
premiums at each age, in Table 15, were obtained. 

It is also manifest from the above that the annual 
premium might have been obtained by the following 
rule : 

Divide the Single Premium by 1 plus the value of 
an annuity on the life at the given age. 

Column R is the sum of the quantity at each age, 
and all the ages older than the given age in column 
M, and is useful in finding the values of increasing 
and decreasing assurances. 



LIFE ANNUITIES.— SINGLE LIVES. 

TABLE XII. 

It has already been shewn, in page 27 that the rates 
2J, 3, and 3^ per cent, in this Table, have been 
constructed from the D and N columns in Tables 9, 
10, and 11, but as D and N columns have not been 
constructed for any other rates of interest, it was 
found to occupy less time to calculate the remaining 
rates by the ordinary method. 

As the payment of an annuity depends upon the 



32 

party being alive when it becomes due, and as an 

annuity is considered to be due at the end of each 

year, it is manifest that the value of an annuity on a 

life aged 99, the oldest age in the Table, is equal to 

; and on a life aged 98, the value, if the life were 

certain to survive the year, would at the end of the 

year be equal to £l, plus an annuity on a life aged 

99, the present value of which reckoning interest 

at 3 per cent, is manifestly. 

1 +0 X .970874 = .970874; but as the life is not certain 

to survive the year, this value must be diminished in 

the ratio of certainty or unity to the probability of its 

surviving the year, and will be 

A . 1 c^n^onA .970874 ^., 
As 1 : |:: .970874 : — - — = .243 

and corresponds with the value given in Table 12, 
under 3 per cent, and opposite to 98 years, and by 
proceeding in this manner from the oldest to the 
youngest age, the rates 2, 4, 4|^, 5, 6, 7, and 8, per 
cent, have been computed, and is the method adopted 
by Mr. Milne in his excellent treatise on annuities. 

The rule being 

Multiply U7iily added to the value of an annuity on 
a life one year older than the given life by the present 
value of £\, due at the end of 1 year, and by the pro- 
bability of the given life surviving 1 year, and the 
product ivill be the value of an annuity on the given 

life. 

The table being formed, the value of any other 
amount at any given age and rate of interest, may 
be readily obtained by the following rule : 



33 

Multiply the anmiity of £\ at the given age and 
rate per cent, by the annuity^ whose amount is required, 
and the product will be the value of such annuity. 

EXAMPLE 1. 

Required the value of an Annuity of ^150 per 
annum, on a life aged 54 reckoning interest at 3 per 
cent ? 

By Table 12, opposite to 54 years of age, will be 
found 12.385. the present value of ^1 per annum on 
a life at that age, which, multiplied by 150 = 
£1857.75 =^1857. 15 the value required 

If it were required to find what annuity should be 
granted in consideration of a sum to be paid down, the 
rule would manifestly be 

Divide the sum to be paid down by the present value 
of an annuity of £\ on the given life at the given rate 
of iideresiy as for 

EXAMPLE 2. 

What Annuity ought to be granted on a life aged 
54 in consideration of jf" 1857. 15 paid down, reckon- 
ing interest at 3 per cent ? 

12.385 was shewn in the last example to be the 
value of an annuity at 3 per cent, on a life 
aged 54. 

1857.75 ^,_ ^ J , 

then .^ oog = X 1 50 Answer, — and corresponds 
12.385 ^ ^ 

with the annuity in example 1, whose present value 
was shewn to be £1857. 75 = f 1857.15. 

E 



34 
LIFE ANNUITIES— JOINT LlV^ES. 

TABLE XIII. 

The same reasoning employed with respect to 
Annuities on Single Lives^ is applicable to Joint 
Lives, the rule to determine the value of an annuity 
on the latter being, 

Multiply unily added to the value of an annuity on 
two Joint LiveSy respectively , one year older than the 
two given lives, by the present value of £\, due at the 
end of one year, and by the probability of the two given 
lives jointly surviving one year, 

EXAMPLE. 

Required, the value of an Annuity on two Joint 
Lives aged 89 and 84, reckoning interest at 3 per 
cent ? 

The two lives one year older than these respectively, 
are aged 90 and 85, and, on reference to Table 13, 
in the column headed, '' Older," will be found 90, 
and in the column on the right, headed, " Younger," 
will be found 85, opposite to which, in the column 
headed, 3 per cent, will be found, 

0.946 the value of an annuity on two joint 
lives, aged 90 and 85, 
And on reference to Table 6, it will be found that 
.7076180 is the probability of a life aged 89, 

surviving one year 
.8103215 ditto 84 years, ditto 



35 



then .7070180 x .8103215 = .57340 the probability 

of the lives jointly 



and by Table 2 .970874 



surviving one year 
present value of <£*! 
at 3 per cent, due at 
the end of one year, 
then 1,946 x .970874 x .57340 = 1.083 the 
value of an annuity on the two lives aged 89 and 
84 as required^ and which corresponds with the value 
in Table 13, opposite to 89 and 84, in column head- 
ed 3 per cent., and in this manner by beginning at 
the ages 



at the several rates of in- 
terest, all the joint lives, 
where the difference of age 
is 5 were obtained, but it 
was not thought necessary 
to print the values of any 
joint lives at an older age 
than 90. 





99 


& M\ 


len 


98 


II 93 


// 


97 


// 92 


if 


m 


// 91 


if 


95 


// 90 


if 


94 


// 89 


If 


93 


// 88 


ff 


92 


// 87 


n 


91 


// 86 


a 


90 


// 85 


H 


89 


// 84 




&c. 


&c. 



And in a similar manner all the other quantities at 
the several rates of interest and differences of age in 
Table 13 were obtained; the value of the oldest of 
the two given lives at the given difference of age 
being first obtained, and then the values of the next 
two respectively, one year younger, &c. 



36 

The Table being formed, the value of an Annuity 
for any amount at any of the given ages, and rates of 
interest, may be obtained in the following manner. 

Multiply the value of the annuity of £\ at the given 
ages and rate of interest by the annuity, ivhose value is 
required, and the product ivill be the value of such 
annuity. 

EXAMPLE 1. 

Required the value of an Annuity of £^0 per 
annum on two joint lives aged 71 & 51, reckoning 
interest at 3|- per cent ? 

On reference to Table 13, in column '' 3 J per 
cent/' opposite to 71 & 51, will be found 5.487, 
which, multiplied by 30, gives 164,610 = ^164 12 2, 
the value required? 

EXAMPLE 2. 

Required the value of an Annuity of £50 per an- 
num on two joint lives aged 7 1 and 53, reckoning 
interest at ^^ per cent ? 

It will be found, on reference to Table 13, that 
both these ages are not contained in the Table, but 
against 71, the older age (in finding the values 
of annuities on joint lives, the older age is the 
index of the two ages), we find opposite to the column 
headed ^* Younger,"' that age 53 falls between 5 1 and 
56, and the value at 3^ per cent, on 
71 & 51 is 5.487 
and 71 // 56 // 5.240 
Dilference 0,247 



37 

and this being the difference for 5 years, 
-|th or, 049 subtracted from 5.487 will give the 

value on 71 & 52 

^^« // 098 ditto ditto, on 71 & 53 

-^ths // 147 ditto ditto, // 71 // 54 

-> // 196 ditto ditto, // 71 // 55 

then 5.487-098 = 5.389, which, multiplied by 50 

= ^269,450 =£"260 9, the value of an annuity of 

£50 per annum on two joint lives, aged 71 & 53, as 

required. 

And in a similar manner the value of an annuity 

at any other ages not found in the Table may be 

obtained. 

TWO JOINT LIVES AND THE SURVIVOR. 

An Annuity on the Last Survivor of two lives 
signifies an Annuity to be paid until the expiration 
of both lives. 

It is manifest that an annuity during the joint conti- 
nuance of two lives added to an annuity on the last 
survivor, are together equal to the sum of similar 
annuities on each of the lives, for in the case of the 
JointLives, the annuity would cease at the first death, 
and in the other on the death of the last survivor, 
consequently the value of the annuity on the last sur- 
vivor may be obtained by subtracting the value of 
an annuity on the Joint Lives from the sum of the 
annuities on the two single lives. 

EXAMPLE. 

Required the value of an Annuity of £30 per 



38 

annum, on the last survivor of two lives aged 51 and 
36, reckoning interest at 3^ per cent? 

On reference to Table 12, in column headed 3 J per 
cent, will be found opposite to ages 5 1 and 36 

12.795 = Value of annuity of jfi'l on a life aged 51, 

17.037 = ditto ditto 36^ 

29.832 = Sum 

And on reference to Table 1 3, in column headed 3j 
per cent, will be found 11.260, the value of an 
annuity on the two joint lives; then 29.832 — 11.260 
= 18.572, which multiplied by 30, gives 55,7160 = 
£65 14 4 — Answer. And in a similar manner the 
value of an annuity of any other amount may be 
obtained, the rule being. 

From the sum of the valuea of an annuity of £\ on 
the separate lives at the given late, deduct the value of 
a similar annuity at the same rate on the Joint Lives 
and midtiply the difference by the annuity whose value 
is required. 



ABSOLUTE REVERSIONS— PRESENT 

VALUES. 

TABLE XIV. 

The mode of constructing this Table is explained 
in page 42. 

EXAMPLE. 

What is the present value of the Reversion to 
^£"5000, or which is the same thing, the Single Pre- 
mium for an assurance of £5000 to be received at 



39 

tlie end of the year, in wliicli a life aged (JO may fail, 
reckoning interest at 4 per cent. ? 

By column 4 per cent, in Table 14, opposite to 60 
years of age will be found .59943, the present value 
of the reversion of ^1 on the failure of the life in 
question ; then 

.59943 X 5000 =^2997.15 =f 2997 3 the value 
required. 

LIFE ASSURANCES— SINGLE LIVES. 
TABLE XV. 
EXAMPLE I, 

What Single Premium should be charged for an 
assurance of f 2500 on a life aged 55, reckoning 
interest at 3 per cent. ? 

By column headed ^^ Single Premium," in Table 
15, and opposite to 55 years of age will be found 
.62075 the Single Premium to assure £l on the given 
life; then ,62075 X 2500 =^155L875 =^1551 17 6, 
the Single Premium required. 

EXAMPLE 2. 

What Annual Premium should be charged for an 
assurance of £4000 on a life aged 65^ reckoning in- 
terest at 3 per cent. ? 

By column headed Annual Premium in Table 15, 
and opposite to 65 years of age, will be found. 07745, 
the Annual premium for an assurance of ^1 on the 
given life, then 

.07745x4000 =^309.8 =.£309 16, the Annual 
Premium required. 



40 

The quantities in Table 15 were obtained by means 
of the D. N, and M, columns in Table 10, as 
explained in pages 28—31. The mode of obtaining 
the same results by the ordinary method will be 
illustrated in the following 

EXAMPLE. 3. 

Required the Single Premium for an assurance of 
^1 on a life aged 97, reckoning interest at 3 per 

cent. 

By Table 2 .970874= Present value of £], to 

be received at the ex- 
piration of 1 year. 
// .942596= ditto ditto, 2 years. 

// .915142= dittoditto, 3 // 

and by Table 5 ^^~^ = Probability of a life aged 

97 failing in or before 
completing the 98th 
year of age. 

^~~^ = ditto ditto, in 99th ditto 



13 

// ^= ditto ditto, in 100th ditto 

Then (see page 28) 

(1^ X .970874) + (^ X .942596) + 

f_i_x .915142) =.96005 Single Premium re- 

^ 13 
quired as contained in Table 15, in column headed 
'' Single Premium/' opposite to 97 years of age. 



41 

Let us, however, separate the positive from the 
negative quantities, and we shall have ( if x .970874) 
+ (^ X 942596) + (i§ X .915142)=Positive quantities. 
If we divide each of these by .970874, the present 
value of ^1, to be received at the expiration of one 
year, and multiply them again by that quantity, 
their value will still be the same, and we shall have 

.970874[j|+(^x 970874) + (j^x942596)| 

But the sum of the two last quantities, as was shewn 
in page 26, is equal to jf 0.37 1— the value of an annu- 
ity on a life aged 97, if, therefore, we substitute this 
value we shall have 

^ + 0.371 )> = 970874 + (.970874 x 0.371) 

Let us now bring down the negative quantities from 
the original expression which are, 

( ^ X 970874) + (^ X 942596) 

But these have just been shewn to be equal to .0.371 
the value of an annuity on a life aged 97, this quan- 
tity, therefore, must be subtracted from the above 
expression, which will give 

,970874 + (.970874 X .0.371) -0.371. 
Now the middle quantity is the present value of 
£0.371 to be received at the expiration of one year, 
(for the present value oi £i due at the end of any 
number of years, multiplied by any other sum, gives 
the present value of that sum for the same period), 
and if we subtract it from the last quantity we shall 
have .01082 or the discount for one year of the value of 



42 

the annuity;* then 970874— .01 082 = .96005, as 
before. 

The rule, therefore, for finding the Single pre- 
mium for an assurance by the ordinary method is 

From the prese7it value of £\ at the given rate of 

interest due at the end of one year subtract the discount 

for one year of the value of an annuity of £\ on the 

given life at the same rate of interest. And by this 

rule the quantities in Table 14 were obtained. 

The Rule to determine the annual premium as 
shewn in page 31, is 

Divide the single premium by 1 plus the value of 
an annuity on the life. 

And in a similar manner it might be shewn, that the 
Rule to determine the Single Premium for an assu- 
rance on two Joint Lives is 

From the present value of £\ at the given rate of 
interest due at the end of one year^ subtract the discount 
for one year of the value of an annuity of £\ on the 
Joint Lives at the same rate of interest. 

And for the Annual Premiums 

Divide the single premium by 1 plus the value of an 
annuity on the Joint Lives. 

And in this manner Table 16 was formed. 

And similarly — 

To find the Single Premium for an Assurance on 
the Last Survivor of Two Lives. 



* The discount of any sum is manifestly the difference between that sum and 
its present value, and may be obtained by multiplying the discount of £1 by 
any other sum, whose discount is required. 



43 

From the present value of £\ at the given rate of 
interest due at the end of one year, subtract the discount 
for one year of the value of an annuity of £\ on the 
last survivor, of the two lives at the same rate of interest. 

And for the Annual Premium — 

Divide the single premium by 1 plus the value of 
an annuity on the last survivor. 

And in this manner Table 17 was formed. 



LIFE ASSURANCES.— JOINT LIVES. 

TABLE XVI. 

The quantities in this Table were constructed by 
the following rules (see page 42.) 

To find the Single Premium. 

From the present value of £\ at the given rate of 
interest, due at the end of one year, subtract the discount 
for one year of the value of an annuity of <£] oji the 
Joint Lives at the same rate of interest. 

To find the Annual Premium : 

Divide the Single Premium by £\ plus the value 
of an annuity on the Joint Lives, 

EXAMPLE 1. 

Required the single and annual premium for an 
assurance of £\ on two lives aged 53 and 18^ rec- 
koning interest at 3 per cent,? 

By column 3 per cent, in Table 2^ and opposite to 
one year^ will be found 



44 

,970874 the present value of ^1 at 3 per cent. 

due at tlie end of one year. 

And 1-. 970874 = .029126 = discount of ^1 at the 

same rate for one year. 

By column 3 per cent in Table 13^ opposite to 53 

and 18, will be found, 

11.776, the value of an annuity of £l on the 

two Joint Lives. 

And .029126 x 1 1.776 = . 34297 = the discount of the 

annuity for one year. 

Then .970874 -.34297 = .62790 the single premium 

required, and corresponds with the quantity in column 

^^ Single Premium," in Table 16, opposite to ages 

53 and 18. 

^ , .62790 .62790 ^.^.. .i a 

1 -1-11 776 ""^ 12 77(3 = .04915 the Annual 

Premium required, and corresponds with the quan- 
tity in column *^ Annual Premium," in Table 16, 
opposite to ages 53 and 18. 

And in a similar manner, the premiums at all the 
other ages in the Table were calculated, from 
which the Premiums, for assurances of any other 
amount may be readily obtained as shewn in the 
following examples. 

EXAMPLE 2. 

Required the Single Premium that would be 
charged according to Table 16, to effect an assu- 
rance of ^2000 on two lives, aged 54 and 29 ? 

On reference to the Table in column, headed 
" Single Premium," and opposite to ages 54 and 29, 



45 

will be found .64306, the Single Premium for an 
assurance of £"1 on the two lives, which, multiplied 
by 2000 gives ^1286.12 =£1286 2 5, the Single 
Premium required. 

EXAMPLE 3. 

What Annual Premium should be charged for the 
above assurance ? 

On reference to Table 16 in column, Annual Pre- 
mium per <£l, and opposite to ages 54 and 29, will 
be found .05247 which multiplied by 2000 = 104.94 
= ^104 18 10, the Annual Premium required. 



LIFE ASSURANCES.— LAST SURVIVOR. 

TABLE XVII. 

The quantities in this Table were constructed by 
the following rules, (see page 42.) 

To find the Single Premium : 

From the present value of £i at the given i^ate oj 

interest clue at the end of one year, subtract the discount 

for one year, of the value of an Annuity of £l on the 

last Survivor of the two lives at the same rate of interest. 

To find the Annual Premium : 

Divide the Single Premium by 1 plus the value of 
an annuity on the last survivor, 

EXAMPLE 1. 

What Single and Annual Premium should be 
charged for an assurance of <£l on the last survivor 



46 

of two lives aged 46 and 41, reckoning interest at 3 
per cent.? 

By Table 12, in column 3 per 
cent, the value of an annuity of ^1, 
on a life aged 46 years is 15.204 

Ditto, ditto, 41 ditto .16.821 

Sum =32.025 

By Table 13, in column 3 per 
cent. the value of an annuity of ^1 
on two joint lives aged 4 6 and 4 lis. . 12.488 

Difference. • 19.537 = Value of 

an annuity of ^1 on the last survivor, (see page 37). 

By Table 2, the present value of £l at 3 per cent, 
due at the end of 1 year = .970874 and 1— .970874 = 
.029126 the discount of ^1 at 3 per cent, for one 
year. 

Then .029126 x 19.537= .56902 the discount 
for one year of the annuity on the last survivor. 
And .97087— .56902 = .40185 = the Single Premium 
required, and corresponds with the quantity in column 
*^^ Single Premium"^ in Table 17, opposite to ages 46 
and 41. 

The Annual Premium, therefore, is equal to 

.40185 .40185 ^^^^^ , , 

1 + 19.537 = 20:537= -^^^^^^ ^^^ corresponds 

with the quantity in column " Annual Premium per 
£{," in Table 17, opposite to the ages 46 and 41. 

And in a similar manner the Premiums at the other 
ages in the Table were found, from which the value of 
an assurance of any other amount may readily be 
obtained as shewn in the following examples. 



47 

EXAMPLE 2. 

What Single Premium should be charged for an 
assurance of £5000 on the last survivor of two lives 
aged 60 and 50^ reckoning interest at 3 per cent.? 

By Table 17_, opposite to ages 60 and 50^ in 
column *^ Single Premium per £\," will be found 
»51671, the single premium for the assurance of £l, 
on the survivor of the two lives^ which_, multiplied by 
5000, gives £2583.55=^2583 11 the single 
premium required, 

EXAMPLE 3. 

What Annual Premium should be charged for the 
above assurance ? 

Bj Table 17^ opposite to ages 60 and 50^ in 
column headed *^ Annual Premium per£j_,''^ will be 
found .03114^ the annual premium for the assurance 
of £l^ on the last survivor of the two lives, which^ 
multiplied by 5000 gives £155.70 = £155 14, the 
annual premium required. 



VALUATION OF POLICIES— SINGLE LIVES. 

TABLES XVIII & XIX. 

Let it be assumed that the Annual Premium upon 
an assurance is ^1. 

Then the value of all the future Premiums_, where 
the Annual Premium has just been paid, is evidently 
equal to the value of an annuity of ^1 on the given 
life. 



48 

And where the premium is just due, but not paid, 
the value is evidently greater by that amount, and is 
equal to ^1 plus the value of an annuity of £l on the 
given life. 

The value of the future premiums, when estimated 
at any intermediate period between two successive 
payments, may, therefore, be obtained by deducting 
the value of ^1 on the age of the assured, at the date 
of the last payment, from the value increased by unity 
of a similar annuity on the age at the next payment, 
and adding to the former a part of the difference, 
proportional to the time elapsed since the last pay- 
ment became due ; and the several values thus ob- 
tained are given for each year and month in Table 18, 

And the value of the future payments of any other 
Annual Premium may be obtained by multiplying the 
quantities in the Table by such Annual Premium. 

The quantities in Table 19, show the Single Pre- 
mium required for an assurance of <£ 1 on each age, 
from 1 to 70 with interpolated values for months 
in each year. 

And the value for any other amount may be 
obtained by multiplying the quantities in the Table 
by such amount. 

The Value of a policy at any time is manifestly the 
difference between the *^ Single Premium,^'' for the 
sum assured on the age of the party, at the time the 
policy is proposed to be valued, and the then value 
of all the future premiums, expected to be received 
on such policy. 



49 



EXAMPLE 1. 

Required the value of a policy of £4000, effected 
at an annual premium of ^100 13 4 = £100.667 on 
a life aged 39, but now aged 57 years and four 
months ? 

By Table 19, in column, headed 4 months, and 
opposite to 57 years, will be found .64561, the single 
premium for an assurance of £l on a life aged 57 
years and 4 months. 

Then .64561 x 4000 = 2582.4= Single Premium for 

an assurance of 

£4000 on a life 

aged 57 years and 

4 months. 

And by Table 18, in column, headed 4 months, and 

opposite to 57 years, will be found 11.501, the value 

of the future premiums of f 1 per annum, on a life 

aged 57 years and 4 months. 

Then 11.501 x 100.667 = 1157.8 = Value of future 

Premiums. 
And 2582.4—1157.8 = 1424.6 = f 1424 12 the 
value of the policy as required. 

EXAMPLE 2. 

Required the value of a policy of £"3000, effected 
at an Annual Premium of ^68 8 0, =68,4 on a life 
aged 36, but now aged 60, upon which the premium 
is just due, but not paid. 

In this case the premium being just due, but not 
paid, the value of the future premiums will be 11.188, 

G 



50 

the quantity in Table 1 8, opposite to 59 years and 
12 months, {i.e. unity added to 10.188, the quantity 
opposite to 60 years of age,) multiplied by 68.4, 
which gives 765.25. 

And by Table 19, the Single Premium for an 
assurance of ^''l, on a life aged 60, is .67414, which, 
multiplied by 3000, is equal to 2022.42. 
Then, 2022.42— 765.25 =£^1257. 17 =£1257 3 5 = 
the present value required. 

If the premium in this case had been just paid, the 
value of the future premiums would be equal to 
10.188, the quantity opposite to 60 years of age mul- 
tiplied by 68.4=696.85. 

And 2022.42-696.85 = 1325.57=^1325 11 5 = 
the value required; which, it will be observed, is 
equal to the above value, plus £6S Ss., so that the 
value of a policy, when the premium has just been 
paid, is equal to the value of the policy upon which 
the premium is due and not paid, plus the payment 
then made. 

If one or more bonuses have been added to a policy, 
find the value at the present age of the sum assured 
by the policy, plus the amount of such bonuses, and 
proceed as before. 

The value of a policy which had been effected by 
the payment of a single premium is manifestly equal 
to the single premium that would be required for an 
assurance of the same amount at the present age, and 
may be obtained from Table 19. 



51 

TEMPORARY ANNUITIES AND 
ASSURANCES. 

Comparative Advantages of the Z), iY, and M Method, and the 
Ordinary Method of Calculating the Values of Annuities 
and Assurances. 
The D and N system was first employed by Mr. 

Griffith Davies^ the Actuary of the Guardian Assu- 
rance Company, and the Formulae used by him are 
somewhat analagous to those originally pointed out by 
the late Mr. Barrett. 

The following examples will serve to show the 
superiority of the new method. 

EXAMPLE 1. 

Required the value of an Annuity of £'20 per 
annum on a life aged 36^ to continue 10 years, reck- 
oning interest at 3 per cent. 

Rule by the D. and N. columns. 

From the quantity in column N at the present as^e, 
subtract the quantity in the same column at the 
advanced a<^e, and divide the difference by the quantity 
in column D at the present age. 

In Table 10, 515312.329 = the quantity in column 

N, opposite to 36 the 

present age. 

,, 287000.704 ditto, opposite to 46, 

■ the advanced age. 

22831 1.625 = difference. 

,, 28228.483 =: the quantity in column 

D. opposite to 36 the 

present age. 



52 

228311.625 ^ ^^^ ,^ 
then "oqooq'Tqq ="*^^"^ ^^^ value required. 

Rule, by the common method — 
From the value of an annuity on the life at the pre- 
sent age, subtract the value of an annuity on the life at 
the advanced age, multiplied hy the present value of£l 
at the given rate of interest due at the end of the term 
for which the annuity is to continue^ and by the proba- 
bility of the life at the present age, surviving that term. 
By column, headed 3 per 

cent, in Table 12 18.255 = present value of 

an annuity of £^1 

on a life aged 36. 

Do. do. 15.204=do. do. 46. 

By Table 2, in column 3 

per cent, opposite 10 years, .744094 = Present value 

of £\ at 3 per 
cent, due at the 
endof 10 years. 

By Table 5 73526 = Probability of a 

81814 life aged 36, 

living 10 years. 

73526 
Then 15.204 x ,744094 x ^YgY^ = 10. i 67 

And 18.255—10.167 =8.088 as before. 

The rule to find the value of a DEFERRED 
ANNUITY, by the D and N columns is. 

Divide the quantity in column N, at the age the 
Annuity is to be entered upon by the quantity in column 
D at the present age. 



53 



EXAMPLE 2. 



Required the Single Premium for an assurance of 
£3000 on a life aged 40 for the term of 7 years, 
reckoning interest at 3 per cent.? 
Rule by the D and M columns. 
From the quantity in column M at the present age 
subtract the quantity in the same column at the advanced 
age, and divide the difference hy the quantity in 
column D at the present age. 

In Table 10, 11384. 144 = the quantity in column 

M, opposite to 40, the 
present age. 
u 9732.454 Ditto opposite to 47 the 

advanced age, 

1651.690 = difference 
u 241 11,6 15= the quantity in column 

D, opposite to 40, the 
present age. 

^, 1651.690 ^^^^ - . , I,. ,. , , 

Ihen 04111 ^ig = '^Q^^^ which, multiplied by 3000 

gives f'205.5=.£'205 10 0, the single premium re- 
quired. 

Rule by the common method. 

From the value of an annuity on the life, at the 
present age, subtract the value of an annuity on the 
life at the advanced age y multiplied by the present value 
of £\. due at the end of the term for which the assur- 
ance is to continue, and by the probability of the life 
surviving that term ; and multiply the difference thus 



54 

obtained by the discount of £ I, for one year; then sub- 
tract this product frofn the present value of £\, due 
at the end of one year, multiplied by unity minus the 
product of the probability of the life surviving the term, 
and the present value of £l, due at the end of the term. 
In column 3 per cent 

of Table 12 17. 123 = the present value of 

an annuity of <£l at 
three per cent, on a 
life aged 40. 
M 14.864= do. do 47 

In ditto of Table 2, .813092 = the present value of 

fl^ at 3 per cent, due 

at the end of 7 years 

Ditto .970874 = do. do. at the end 

of 1 year. 
And 1—970874 = 029 126= discount of£l at 3 

per cent, for one year. 
From Table 5 we obtain 4lil, the probability of a 
life aged 40 surviving 7 years. 

From which we obtain, according to the rule 

.970874[l— ^mi X .813092 |-.029126J^17.I23— 






-ggx. 813092x14.864] = 



.24240— .17388 = .06852. 
And .06852 x 3000- £205.5 = £205 10 as before. 

The rule to find the value of a DEFERRED 
ASSURANCE by the D and M columns is, 



55 

Divide the quantity in column M, at the advanced 
age, by the quantity in column D at the present age. 

The above examples in Temporary Annuities^ and 
Assurances, without exhibiting the length of the 
operations of the multiplications and divisions, are 
sufficiently illustrative of the superiority of the D and 
N method. Other examples, much more striking, 
might be given, but the subject will be found fully 
illustrated in the treatise on Annuities and Assu- 
rances, by D. Jones, published by the Society for the 
Diffusion of Useful Knowledge, in which will also be 
found a very extensive collection of formulae for all 
cases involving one and two lives.* 



*This Formulae is contained in No. 7, of the work, price sixpence, which may 
probably be obtained separately, and as it is printed in octavo, it might with 
advantage be bound up with the present work. 



TAB LES 



COMPOUND INTEREST, 

Showing the Amount of £1 improved at Compound Interest, for any 
number of years not exceeding 100. 



Years. 



1 
2 
3 
4 
5 

G 
7 
8 
9 
10 

11 
12 
13 
14 
15 

16 
17 
18 
19 

20 

21 
22 
23 
24 
25 

26 
27 
28 
29 
30 

31 
32 
33 
34 
35 

36 

37 
38 
39 
40 

41 
42 
43 
44 
45 

46 
47 
48 
49 
50 



1 ^ Cent. 



li ^ Cent. 2 W Cent 



2i W Cent. 



1.010000 
1.020100 
1.030301 
1.040604 
1.051010 

1.061520 
1.072135 
1.082856 
1.093685 
1.104622 

1.115668 
1.126825 
1.138093 
1.149474 
1.160969 

1.172579 
1.184305 
1.196148 
1.208109 
1.220190 

1.232392 
1.244716 
1.257163 
1 269735 

1.282432 

1.295256 
1.308209 
1.321291 
1.334504 
1.347849 

1.361327 
1.374940 
1.388689 
1.402576 
1.416602 

1.430768 
1.445076 
1.459527 
1.474122 

1.488863 

1.503752 
1.518790 
1.533978 
1.549318 
1.. 5648 11 

1.580459 
1.596264 
1.612227 
1.628349 
1.644632 



1.015000 
1.030225 
1.045678 
1.061363 
1.077284 

1.093444 
1.109845 
1.126492 
1.143389 
1.160540 

1.177948 
1.195616 
1.213550 
1.231754 
1.250231 

1.268984 I 

1.288019 

1.307339 

1.326948 

1.346851 

1.367055 
1.387562 
1.408376 
1.429502 
1.450945 

1.472709 
1.494800 
1.517222 
1.539980 
1.563080 

1.586527 
1.610324 
1.634479 
1.658997 
1.683882 

1.709141 
1.734777 
1.760799 
1.787211 
1.814019 

1.841229 
1.868847 
1.896879 
1.925333 
1.954212 

1.983525 
2.013277 
2.043477 
2.074129 
2.105240 



1.020000 
1.040400 
1.061208 
1.082432 
1.104081 

1.126162 
1.148686 
1.171659 
1.195093 
1.218994 

1.243374 
1.268242 
1.293607 
1.319479 
1.345868 

1.372786 
1.400241 
1.428246 
1.456811 
1.485947 

1.515666 
1.545980 
1.576899 
1.608437 
1.640606 

1.673418 
1.706886 
1.741024 
1.775845 
1.811362 

1.847589 
1.884541 
1.922231 
1.960076 
1.999890 

2.039887 
2.080685 
2.122299 
2.164745 
2.208040 

2.252200 
2.297244 
2.343189 
2.390053 
2.437854 

2.486611 
2.536344 

2.587070 
2.638812 
2.691588 



3#'Cent. Sic^Cent. 



1.025000 
1.050625 
1.076891 
1.103813 
1.131408 

1.159693 
1.188686 
1.218403 
1.248863 
1.280085 

1.312087 
1.344889 
1.378511 
1.412974 
1.448298 

1.484506 
1.521618 
1.559659 
1.598650 
1.638616 

1.679582 
1.721571 
1.764611 
1.808726 
1.853944 

1.900293 
1.947800 
1.996495 
2.046407 
2.097568 

2.150007 
2.203757 
2.258851 
2.315322 
2.373205 

2.432535 
2.493349 
2.555682 
2.619574 
2.685064 

2.752190 
2.820995 
2.891520 
2.963808 
3.037903 

3.113851 
3.191697 
3.271490 
3.353277 
3.437109 



1.030000 
1.060900 
1.092727 
1.125509 
1.159274 

1.194052 
1.229874 
1.266770 
1.304773 
1.343916 

1.384234 
1.425761 
1.468534 
1.512590 
1.557967 

1.604706 
1.652848 
1.702433 
1.753506 
1.806111 

1.860295 
1.916103 
1.973587 
2.032794 
2.093778 

2.156591 
2.221289 
2.287928 
2.356566 
2.427262 

2.500080 
2.575083 
2.652335 
2.731905 
2.813862 

2.898278 
2.985227 
3.074783 
3.167027 
3.262038 

3.359899 
3.460696 
3.564517 
3.671452 
3.781596 

3.895044 
4.011895 
4.132252 
4.256219 
4.383906 



1.035000 
1.071225 
1.108718 
1.147523 
1.187686 

1.229255 
1.272279 
1.316809 
1.362897 
1.410599 

1.459970 
1.511069 
1.563956 
1.618695 
1.675349 

1.733986 
1.794676 
1.857489 
1.922501 
1.989789 

2.059431 
2.131512 
2.206114 
2.283328 
2.363245 

2.445959 
2.531567 
2.620172 
2.711878 
2.806794 

2.905031 
3.006708 
3.111942 
3.220860 
3.333590 

3.450266 
3.571025 
3.696011 
3.825372 
3.959260 

4.097834 
4.241258 
4.389702 
4.543342 
4.702359 

4.866941 
5.037284 
5.213589 
5.396065 
5.584927 



TABXiS X. 

COMPOUND INTEREST, 

Showing the Aiiiount of£l im})roved at Compoun<l Interest, for any 
number of vears not exceedinnr 100. 



Years 


. 4 #" Cent. 


4^ #• Cent 


. 5#'Cent. 


6 f Cent. 


7 4f Cent. 


8 ^ Cent. 


1 


1.040000 


1.045000 


1.050000 


1.060000 


1.070000 


1.080000 


o 


1.081000 


1.092025 


1.102500 


1.123600 


1.144900 


1.166400 


3 


1.124864 


1.141166 


1.157625 


1.191016 


1.225043 


1.259712 


4 


1.169859 


1.192519 


1.215506 


1.262477 


1.310796 


1.360489 


5 


1.216653 


1.246182 


1.276282 


1.338226 


1.402552 


1.469328 


6 


1.265319 


1.302260 


1.340096 


1.418519 


1.500730 


1.586874 


7 


1.315932 


1.360862 


1.407100 


1.503630 


1.605781 


1.713824 


8 


1.368569 


1.422101 


1.477455 


1.593848 


1.718186 


1.850930 


9 


1.423312 


1.486095 


1.551328 


1.689479 


1.8384.59 


1.999005 


10 


1.480244 


1.552969 


1.628895 


1.790848 


1.967151 


2.158925 


11 


1.539454 


1.622853 


1.710339 


1.898299 


2.104852 


2.331639 


12 


1.601032 


1.695881 


1.795856 


2.012196 


2.252192 


2.518170 


13 


1 .665074 


1-772196 


1.885649 


2.132928 


2.409845 


2.719624 


14 


1.731676 


1.851945 


1.979932 


2.260904 


2.578534 


2.937194 


15 


1.800944 


1.935282 


2.078928 


2.396558 


2.759032 


3.172169 


16 


1.872981 


2.022370 


2-182875 


2.540352 


2.952164 


3.425943 


17 


1-947901 


2.113377 


2.292018 


2.692773 


3.158815 


3.700018 


18 


2.025817 


2.208479 


2-406619 


2.854339 


3.379932 


3.996020 


19 


2.106849 


2.307860 


2.526950 


3.025600 


3.616528 


4.315701 


20 


2.191123 


2,411714 


2.653298 


3.207135 


3.869684 


4.660957 


21 


2-278768 


2.520241 


2-785963 


3.399564 


4.140562 


5.0.338.34 


22 


2.369919 


2.633652 


2.925261 


3.603537 


4.430402 


5.436540 


23 


2-464716 


2.752166 


3.071524 


3.819750 


4.740530 


5.871464 


24 


2.563304 


2.876014 


3.225100 


4.048935 


5.072367 


6.341181 


25 


2.665836 


3.005434 


3.386355 


4.291871 


5-427433 


6.848475 


2G 


2.772470 


3.140679 


3.555673 


4-549383 


5-807353 


7.396353 


27 


2.883369 


3.282010 


3-733456 


4.822346 


6.213868 


7.988061 


28 


2.998703 


3.429700 


3.920129 


5.111687 


6.648838 


8.627106 


29 


3.118651 


3.584036 


4.116136 


5.418388 


7.114257 


9.317275 


30 


3.243398 


3.745318 


4-321942 


5.743491 


7.612255 


10.062657 


31 


3-373133 


3.913857 


4.538039 


6.088101 


8.145113 


10.867669 


32 


3.508059 


4.089981 


4.764941 


6.453387 


8.715271 


11.737083 


33 


3.648381 


4.274030 


5.003189 


6.840590 


9.325340 


12.676050 


34 


3-794316 


4.466362 


5.253348 


7.251025 


9.978114 


13.6901.34 


35 


3-946089 


4.667348 


5.516015 


7.686087 


10.676581 


14.78.5344 


36 


4.103933 


4.877378 


5.791816 


8.147252 


11.423942 


15.968172 


37 


4.268090 


5.096860 


6.081407 


8.636087 


12.22.3618 


17.245626 


38 


4.438813 


5.326219 


6.385477 


9.154252 


13.079271 


18.625276 


39 


4-616366 


5.565899 


6.704751 


9.703507 


13.994820 


20.115298 


40 


4-801021 


5.816365 


7.039989 


10.285718 


14.974458 


21.724522 


41 


4.993061 


6.078101 


7.391988 


10.902861 


16.022670 


23--162483 


42 


5.192784 


6.351615 


7.761588 


11.557033 


17.144257 


25-339482 


43 


5-400495 


6.637438 


8.149667 


12.250455 


18.344355 


27-366640 


44 


5.616515 


6.936123 


8.557150 


12.985482 


19.628460 


29-555972 


45 


5.841176 


7.248248 


8.985008 


13.764611 


21.002452 


31.920449 


46 


6.074823 


7.574420 


9.434258 


14.590487 


22.472623 


34.474085 


47 


6.317816 


7.915268 


9.905971 


15.465917! 


24.045707 


37.232012 


48 


6.570528 


8.271456 


10.401270 


16.393872 


25.728907 


40-210573 


49 


6.833349 


8.643671 


10.921333 


17.377504 ' 


27.529930 


43.427419 


50 


7.106683 


9.032636 


11.407400 


18.420154 


29.457025 46.9016131 



TABXiZ: X. 

COMPOUND INTEREST, 

Showing the Amount of £1 improved at Compound Interest, for anj 
number of years not exceeding 100. 





Years. 


1 #• Cent. 


li f Cent. 


2 #• Cent. 21 #" Cent. 


3 W Cent. 3i f Cent. 

1 




51 


1.661078 


2.136818 


2.745420 


3.523036 


4.515423 


5.780399 




52 


1.677689 


2.168870 


2.800328 


3.611112 


4.650886 


5.982713 




63 


1.694466 


2.201404 


2.856335 


3.701390 


4.790412 


6.192108 




54 


1.711411 


2.234425 


2.913461 


3.793925 


4.934125 


6.408832 




55 


1.728525 


2.267946 


2.971731 


3.888773 


5.082149 


6.633141 




56 


1.745810 


2.301964 


3.031165 


3.985992 


5.234613 


6.8^5301 




57 


1.763268 


2.336494 


3.091789 


4.085642 


5.391651 


7.105587 




58 


1.780901 


2.371541 


3.153624 


4.187783 


5.553401 


7.354282 




59 


1.798710 


2.407114 


3.216697 


4.292478 


5.720003 


7.611682 




60 


1.816697 


2.443220 


3.281031 


4.399790 


5.891603 


7.878091 




61 


1.834864 


2.479868 


3.346651 


4.509784 


6.068351 


8.153824 




62 


1.853213 


2.517067 


3.413584 


4.622529 


6.250402 


8.439208 




63 


1.871745 


2.554823 


3.481856 


4.738092 


6.437914 


8.734580 




64 


1.890462 


2.593145 


3.551493 


4.856545 


6.631051 


9.040291 




65 


1.909367 


2.632042 


3.622523 


4.977958 


6.829983 


9.356701 




66 


1.928461 


2.671522 


3.694974 


5.102407 


7.034882 


9.684185 




67 


1.947746 


2.711594 


3.768873 


5.229967 


7.245929 


10.023132 




68 


1.967223 


2.752267 


3.844251 


5.360717 


7.463307 


10.373941 




69 


1.986895 


2.793550 


3.921136 


5.494734 


7.687206 


10.737029 




70 


2.006764 


2.835454 


3.999558 


5.632103 


7.917822 


11.112825 




71 


2.026832 


2.877986 


4.079549 


5.772905 


8.155357 


11.501774 




72 


2.047100 


2.921156 


4.161140 


5.917228 


8.400017 


11.904336 




73 


2.067571 


2.964974 


4.244363 


6.065159 


8.652018 


12.320988 




74 


2.088247 


3.009449 


4.329250 


6.216788 


8.911578 


12.752223 




75 


2.109129 


3.054590 


4.415835 


6.372207 


9.178926 


13.198550 




76 


2.130220 


3.100409 


4.504152 


6.531513 


9.454293 


13.660500 




77 


2.151522 


3.146913 


4.594235 


6.694800 


9.737922 


14.138617 




78 


2.173037 


3.194117 


4.686120 


6.862170 


10.030060 


14.633469 




79 


2.194767 


3.242029 


4.779842 


7.033725 


10.330962 


15.145640 




80 


2.216715 


3.290659 


4.875439 


7.209568 


10.640891 


15.675738 




81 


2.238882 


3.340020 


4.972948 


7.389807 


10.960117 


16.224388 




82 


2.261271 


3.390120 


5.072407 


7.574552 


11.288921 


16.792242 




83 


2.283884 


3.440971 


5.173855 


7.763916 


11.627588 


17.379970 




84 


2.306723 


3.492586 


5.277332 


7.958014 


11.976416 


17.988269 




85 


2.329790 


3.544975 


5.382879 


8.156964 


12.335709 


18.617859 




86 


^ 2.353088 


3.598150 


5.490536 


8.360888 


12.705780 


19.269484 


1 87 


2.376619 


3.652123 


5.600347 


8.569911 


13.086953 


19.943916 


i 88 


2.400385 


3.706905 


5.712354 


8.784158 


13.479562 


20.641953 




89 


2.424389 


3.762509 


5.826601 


9.003762 


13.883949 


21.364421 




90 


2.448633 


3.818947 


5.943133 


9.228856 


14.300467 


22.112176 




91 


2.473119 


3.876231 


6.061996 


9.459578 


14.729481 


22.886102 




92 


2.497850 


3.934374 


6.183236 


9.696067 


15.171366 


23.687116 




93 


2.522828 


3.993390 


6.306900 


9.938469 


15.626507 


24.516165 




94 


2.548056 


4.053291 


6.433038 


10.186931 


16.095302 


25.374230 




95 


2.573537 


4.114090 


6.561699 


10.441604 


16.578161 


26.262329 




96 


2.599272 


4.175800 


6.692933 


10.702644 


17.075506 


27.181510 




97 


2.625265 


4.238437 


6.826792 


10.970210 


17.587771 


28.132863 




98 


2.651518 


4.302013 


6.963328 


11.244465 


18.115404 


29.117513 




99 


2.678033 


4.366543 


7.102594 


11.525577 


18.658866 


30.136626 




100 


2.704813 


4.432041 


7.244646 


11.813716 1 19.218632 1 31.191408 



TABZ«E X. 

COMPOUND INTEREST, 

Showing the Amount of £1 improved at Compound Interest, for any 
number of years not exceeding 100. 



Years 

51 
52 
53 
54 
55 

56 

57 
58 
59 
60 

61 

62 
63 

64 i 

65 j 

66 ! 
67 
68 
69 
70 

71 
72 
73 
74 
75 

76 

77 
78 
79 
80 

81 
82 
83 
84 
85 

86 

87 



4 4P' Cent. !4^ #* Cent, 



89 
90 

91 
92 
93 
94 
95 

9G 
97 
98 
99 
100 



7.390951 
7.686589 
7.994052 
8.313814 
8.646367 

8.992222 

9.351910 

9.725987 

10.115026 

10.519627 

10.940413 
11.378029 
11.833150 
12.306476 
12.798735 

13-310685 
13.843112 
14.396836 
14.972710 
15.571618 

16.194483 
16.842262 
17.515953 
18.216591 
18.945255 

19.703065 
20.491187 
21.310835 
22.163268 
23.049799 

23.971791 
24.930663 
25.927889 
26.965005 
28.043605 

29.165349 
30.331963 
31.545242 
32.807051 
34.119333 

35.484107 
.36.903471 
38.379610 
39.914794 
41.511386 

43.171841 
I 44.898715 
46.694664 
48.562450 
50.504948 



9.439105 

9.863865 

10.307739 

10.771587 

11.256308 

11.762842 
12.292170 
12.845318 
13.423357 
14.027408 



5 ^ Cent. 6 ^ Cent 



14.658641 
15.318280 
16.007603 
16.727945 
17.480702 

18.267334 
19.089364 
19.948385 
20.846063 
21.784136 

22.764422 

23.788821 
24.859318 
25.977987 
27.146996 

28.368611 
29.645199 
30.979233 
32.373298 
33.830096 

35.352451 
36.943311 
38.605760 
40.343019 
42.158455 

44.055586 
46.038087 
48.109801 
50.274742 
52.537105 

54.901275 
57.371832 
59.953565 
62.651475 
65.470792 

68.416977 
71.495741 
74.713050 
78.075137 
81.588518 



7 #' Cent. 8 ^ Cent 



12.040770 
12.642808 
13.274949 
13.938696 
14.635631 

15.367412 
16.135783 
16.942572 
17.789701 
18.679186 

19.613145 
20.593802 
21.623493 
22.704667 
23.839901 

25.031896 
26.283490 
27.597665 
28.977548 
30.426426 

31.947747 
33.545134 
35.222391 
36.983510 
38.832686 j 

40.774320 
42.813036 
44.953688 
47.201372 
49.561441 

52.039513 
54.641489 
57.373563 
60.242241 
63.254353 

66.417071 
69.737925 
73.224821 
76.886062 
80.730365 



50 053742 
54*706041 
59'082524 
63" 8091 26 
68*91 3856 

74.426965 
80.381122 
86.811612 
93.756540 
101.257064 



31.5190171 
33.725348 
36.086122 
38.612151 
41.315001 

44.207052 
47.301545 
50.612653 
54.155539 
57.946427 

62.0026771109.357629 
66.342864 118.106239 
70.986865 127.554738 
75.955945 137.759117 
81.272861 148.779847 

86.961962 160.682234 

93.049299173.536813 

99.562750 187.419758 

106.532142 202.413339 

113.989392 218.606406 

121.968650 236.094918 
130.506455 254.982512 



19.525364] 
20.6968851 
21.9386981 
23.255020 1 
24.650322 

26.129341 
27.697101 
29.358927 
31.120463 
32.987691 

34.966952 
37.064969 
39.288868 
41.646200 
44.144972 

46.793670 
49.601290 
52.577368 
55.732010 
59.075930 

62.620486 
66.377715 
70.360378 
74.582001 
79.056921 

83.800336 
88.828356 
94.158058 
99.807541 
105.795993 

112.143753 
118.872378 
126.004721 
133.565004 
141.578904 

150.073639 
159.078057 
168.622740 
178.740105 
189.46451l|441.102980ll018.91509 



139.641907 
149.416840 
159.876019 

171.067341 
183.042054 
195.854998 
209.564848 
224.234388 

239.930795 
256.725950 
274.696767 
293.925541 



275.381113 
297.411602 
321.204530 

346.900892 
374.652964 
404.625201 
436.995217 
471.954834 

509.711221 
550.488119 
594.527168 
642.089342 



314.500328 693.456489 

336.515351748.933008 
360.071426 808.847649 
385.276426;873.555461 
412.2457761943.439897 



84.7668831200.832382 471.980188 1100.42830 



505.018802,1188.46256 
540.370118 11283.53956 
578.196026 1386.22273 
618.669748 1497.12055 



89.005227,212.882325 
93.455489 225.655264 
98.1282631239.194580 
103.0346761253.546255 

108.186410,268.759030 661.976630 1616.89019 
1 13.595731 1284.884572 708.314994 1746.24141 
119.275517 301.977646,757.897044 1885.94072 
125.239293 320.096305 810.949837 2036.81.598 
131.5012.58 3.39.302084'867. 716326 2199.76126 



TikB£.£S IZ, 

DEFERRED SUxMS CERTAIN, 

Showing the Present Value of £1 to he received at the end of anY 
number of years not exceeding 100. 



Years. 
1 


1 #" Cent. 


li<^Cent. 


2 ^ Cent. 


21 ^ Cent. 


3 f Cent.' 


3i #• Cent. 


.990099 


.985222 


.980392 


.975610 


.970874 


.9661 8^ 


2 


.980296 


.970662 


.9(51169 


.951814 


.942596 


.933511 


3 


.970590 


.956317 


.942322 


.928599 


.915142 


.901943 


4 


.960980 


.942184 


.923845 


.90595] 


.888487 


.871442 


5 


.951466 


.928260 


.905731 


.883854 


.862609 


.841973 


6 


.942045 


.914542 


.887971 


.862297 


.837484 


.813501 


7 


.932718 


.901027 


.870560 


.841265 


.813092 


.785991 


8 


.923483 


.887711 


.853490 


.820747 


.789409 


.759412 


9 


.914340 


.874592 


.836755 


.800728 


.766417 


.733731 


10 


.905287 


.861667 


.820348 


.781198 


.744094 


.708919 


11 


.896324 


.848933 


.804263 


.762145 


.722421 


.684946 


12 


.887449 


.836387 


.788493 


.743556 


.701380 


.661783 


13 


.878662 


.824027 


.773033 


.725420 


.680951 


.639404 


14 


.869963 


.811849 


.757875 


.707727 


.061118 


.617782 


15 


.861349 


.799852 


.743015 


.690466 


.641862 


.596891 


16 


.852821 


.788031 


.728446 


.673625 


.623167 


.576706 


17 


.844377 


.776385 


.714163 


.657195 


.605016 


.557204 


18 


.836017 


.764912 


.700159 


.641166 


.587395 


.538361 


19 


.827740 


.753607 


.686431 


.625528 


.570286 


.520156 


20 


.819544 


.742471 


.672971 


.610271 


.553676 


.502566 


21 


.811430 


.731498 


.659776 


.595386 


.537549 


.485571 


22 


.803396 


.720687 


.646839 


.580865 


.521893 


.469151 


23 


.795442 


.710037 


.634156 


.566697 


.506692 


.453286 


24 


.787566 


.699544 


.621721 


.552875 


.491934 


.437957 


25 


.779768 


.689206 


.609531 


.539391 


.477606 


.423147 


26 


.772048 


.679020 


.597579 


.526235 


.463695 


.408838 


27 


.764404 


.668986 


.585862 


.513400 


.450189 


.395012 


1 *-28 


.756836 


.659099 


.574375 


.500878 


.437077 


.381654 


1 29 


.749342 


.649359 


.563112 


.488661 


.424346 


.368748 


1 ^^ 


.741923 


.639762 


.552071 


.476743 


.411987 


.356278 


1 31 


.734577 


.630308 


.541246 


.465115 


.399987 


.344230 


1 32 


.727304 


.620994 


.530633 


.453771 


.388337 


.332590 


1 33 


.720103 


.611816 


.520229 


.442703 


.377026 


.321343 


34 


.712973 


.602774 


.510028 


.431905 


.366045 


.310476 


35 


.705914 


.593866 


.500028 


.421371 


.355383 


.299977 


36 


.698925 


.585090 


.490223 


.411094 


.345032 


.289833 


37 


.692005 


.576443 


.480611 


.401067 


.334983 


.280032 


38 


.685153 


.567924 


.471187 


.391285 


.325226 


.270562 


39 


.678370 


.559531 


.461948 


.381741 


.315754 


.261413 


40 


.671653 


.551262 


.452890 


.372431 


.306557 


.252572 


41 


.665003 


.543116 


.444010 


.363347 


.297628 


'244031 


42 


.658419 


.535089 


.435304 


.354485 


.288959 


•235779 


43 


.651900 


.527182 


.426769 


.345839 


.280543 


•227806 


44 


.645445 


.519391 


.418401 


.337404 


.272372 


•220102 


45 


.639055 


.511715 


.410197 


.329174 


.264439 


•212659 


46 


.632728 


.504153 


•402154 


•321146 


.256737 


.205468 


47 


.626463 


.496702 


.304268 


•313-313 


.249259 


.198520 


48 


.620260 


.489362 


.386538 


•305671 


.241999 


.191806 


49 


.614119 


.482130 


.378958 


.298216 


.234950 


.185320 


1 50 


.608039 


.475005 


.371528 


.290942 


.228107 


.179053 



TABXiS XX. 

DEFERllED SUMS CERTAIN, 

Showing the Present Value of £1 to be received at the end of any 

number of years not exceeding 100. 



Years. 
1 


4 #■ Cent. A 


li #• Cent.i 


5 ^ Cent. 


6 W Cent. 


7 W Cent. 


8 W Cent. 


.961538 


.956938 


.952381 


.943396 


.934579 


.92.5926 


2 


.924556 


.91573;) 


.907029 


.889996 


.873439 


.857339 


3 


.888996 


.876297 


.863838 


.839619 


.816298 


.793832 


4 


.854804 


.838561 


.822702 


.792094 


.762895 


.73.5030 


5 


.821927 


.802451 


.783526 


.747258 


.712986 


.680583 


G 


.790315 


.767896 


.746215 


.704961 


.666342 


.630170 


7 


.759918 


.734828 


.710081 


.665057 


.622750 


.583490 


8 


.730690 


.703185 


.676839 


.627412 


.582009 


.540209 


9 


.702587 


.672904 


.644609 


.591898 


.543934 


..500249 


10 


.675564 


.643928 


.613913 


.558395 


.508349 


.463193 


11 


.649581 


.616199 


.584679 


.526788 


.475093 


.428883 


12 


.624597 


.589664 


.556837 


.496969 


.444012 


.397114 


13 


.600574 


.564272 


.530321 


.468839 


.414964 


.367698 


14 


.577475 


.539973 


.505068 


.442301 


.387817 


.340461 


15 


.555265 


.516720 


.481017 


.417265 


.362446 


.315242 


16 


.533908 


.494469 


.458112 


.393646 


.338735 


.291890 


17 


.513373 


.473176 


.436297 


.371364 


.316574 


.270209 


18 1 


.493628 


.452800 


.415521 


.350344 


.295864 


.250249 


19 


.474642 


.433302 


.395734 


.330513 


.276508 


.231712 


20 


.456387 


.414643 


.376889 


.311805 


.258419 


.214.548 


21 


.438834 


.396787 


.358942 


.294155 


.241513 


.198656 


22 


.421955 


.379701 


.341850 


.277505 


.225713 


.183941 


23 


.405726 


363350 


.325571 


.261797 


.210947 


.170315 


24 


.390121 


347703 


.310068 


.246979 


.197147 


.157699 


25 


.375117 


.332731 


.295303 


.232999 


.184249 


.146018 


26 


.360689 


•318402 


.281241 


.219810 


.172195 


.135202 


27 


.346817 


.304691 


.267848 


.207368 


.160930 


.12.5187 


28 


.3.33477 


.291571 


.255094 


.195630 


.150402 


.115914 


29 


.320651 


.279015 


.242946 


.184557 


.140563 


.107328 


30 


.308319 


.267000 


.231377 


.174110 


.131367 


.099377 


31 


.296460 


.255502 


.220359 


.164255 


.122773 


.092016 


32 


.285058 


.244500 


.209866 


.154957 


.114741 


.085200 


33 


.274094 


.233971 


.199873 


.146186 


.107235 


.078889 


tJKJ 

34 


.263552 


,223896 


.190355 


.137912 


.100219 


.07.3045 


35 


.253415 


.214254 


.181290 


.130105 


.093663 


.067635 


36 


.243669 


.205028 


.172657 


.122741 


.087535 


.062625 


37 


.234297 


.196199 


.164436 


,115793 


.081809 


.057986 


tJ 9 

38 


.225285 


.187750 


.156605 


.109239 


.076457 


.053690 


39 


.216621 


.179665 


.149148 


.103056 


.071455 


.049713 


40 


.208289 


.171929 


.142046 


.097222 


.066780 


.046031 

1 


41 


.200278 


.164525 


.135282 


.091719 


.062412 


.042621 


42 


.192.575 


.157440 


.128840 


.086527 


.058329 


.039464 


43 


.185168 


.150661 


.122704 


.081630 


.054513 


.036541 


44 


.178046 


.144173 


.116861 


.077009 


.050946 


.033834 


45 


.171198 


.137964 


.111297 


.072650 


1 .047613 


.031328 


4fi 


.164614 


.132023 


.105997 


.068538 


.044499 


i .029007 


47 
48 
49 
50 


.158283 


.126338 


.100949 


.064658 


.041587 


1 .026859 


.1.52195 


.120898 


.096142 


.060998 


.038867 


1 .024869 


.146341 


.115692 


.091564 


.057546 


.036324 


! .023027 


.140713 


.110710 


.087204 


.054288 


' .033948 


.021321 



TABX.X: xz. 

DEFERRED SUMS CERTAIN, 

Showing the Present Value of £1 to be received at the end of any 
number of years not exceeding 100. 



Years. 


1 #* Cent. 


l^c^Cent. 


2#^Cent. 1 


2^ ^ Cent. 


1 
3 W Cent. 


3i W Cent 


51 


,602019 


.467985 


.364243 


.283846 


.221463 


.172998 


52 


.596058 


.461069 


.357101 


.276923 


.215013 


.167148 


53 


.590156 


.454255 


.350099 


.270169 


.208750 


.16149C 


54 


.584313 


.447542 


.343234 


.263579 


.202670 


.156035 


55 


.578528 


.440928 


.336504 


.257151 


.196767 


.150758 


56 


.572800 


.434412 


.329906 


.250879 


.191036 


.145660 


57 


.567129 


.427992 


.323437 


.244760 


.185472 


.140734 


58 


.561514 


.421661 


.317095 


.238790 


.180070 


.135975 


59 


.555954 


.415435 


.310878 


.232966 


.174825 


.131377 


60 


.550450 


.409296 


.304782 


.227284 


.169733 


.126934 


61 


.545000 


.403247 


.298806 


.221740 


.164789 


.122642 


62 


.539604 


.397288 


.292947 


.216332 


.159990 


.118495 


63 


.534261 


.391417 


.287203 


.211055 


.155330 


.114487 


64 


.528971 


.385632 


.281572 


.205908 


.150806 


.110616 


65 


.523734 


.379933 


.276051 


.200886 


.146413 


.106875 


66 


.518548 


.374318 


.270638 


.195986 


.142149 


.103261 


67 


.513414 


.368787 


.265331 


.191206 


.138009 


.099769 


68 


.508331 


.363337 


.260129 


.186542 


.133989 


.096395 


69 


.503298 


.357967 


.255028 


.181992 


.130086 


.093136 


70 


.498315 


.352677 


.250028 


.177554 


.126297 


.089986 


71 


.493381 


.347465 


.245125 


.173223 


.122619 


.086943 


72 


.488496 


.342330 


.240319 


.168998 


.119047 


.084003 


73 


.483659 


.337271 


.235607 


.164876 


.115580 


.081162 


74 


.478871 


.332287 


.230987 


.160855 


.112214 


.078418 


75 


.474130 


.327376 


.226458 


.156931 


.108945 


.075766 


76 


.469435 


.322538 


.222017 


.153104 


.105772 


.073204 


77 


.464787 


.317771 


.217664 


.149370 


.102691 


.070728 


78 


.460185 


.313075 


.213396 


.145726 


.099700 


.068337 


79 


.455629 


.308449 


.209212 


.142172 


.096796 


.066026 


80 


.451118 


.303890 


.205110 


.138705 


.093977 


.063793 


81 


.446651 


.299399 


.201088 


.135322 


.091240 


.061636 


82 


.442229 


.294975 


.197145 


.132021 


.088582 


.059551 


83 


.437851 


.290616 


.193279 


.128801 


.086002 


.057538 


84 


.433516 


.286321 


.189490 


.125659 


.083497 


.055592 


85 


.429223 


.282089 


.185774 


.122595 


.081065 


.053712 


86 


.424973 


.277920 


.182132 


.119605 


.078704 


.051896 


87 


.420766 


.273813 


.178560 


.116687 


.076412 


.050141 


88 


.416600 


.269767 


.175059 


.113841 


.074186 


.048445 


89 


.412475 


.265780 


.171627 


.111065 


.072026 


.046807 


90 


.408391 


.261852 


.168261 


.108356 


.069928 


.045224 


91 


.404348 


.257983 


.164962 


.105713 


.067891 


.043695 


92 


.400344 


.254170 


.161728 


.103135 


.065914 


.042217 


93 


.396380 


.250414 


.158556 


.100619 


.063994 


.040789 


94 


.392456 


.246713 


.155448 


.098165 


.062130 


.039410 


95 


.388570 


.243067 


.152400 


.095771 


.060320 


.038077 


96 


.384723 


.239475 


.149411 


.093435 


.058563 


.036790 


97 


.380914 


.235936 


.146482 


.091156 


.056858 


.035546 


98 


.377142 


.232449 


.143610 


.088933 


.055202 


.034344 


99 


.373408 


.229014 


.140794 


.086764 


.053594 


.033182 


100 


.369711 


.225629 


.138033 


.084647 


.052033 


.032060 



TABXaS ZZ. 

DEFERRED SUMS CERTAIN, 

Showing the Present Value of £1 to be received at the end of any 
number of years not exceeding 100. 



Years. 


4^ Cent. 


4i ^ Ceut. 


5 #* Cent. 


6 ^ Cent. 


7 ^ Cent. 


8 ^ Cent. 


51 


.135301 


.105942 


.083051 


.051215 


.031727 


.019742 


52 


.130097 


.101380 


.079096 


.048316 


.029651 


.018280 


53 


.125093 


.097014 


.075330 


.045582 


.027711 


.016925 


54 


.120282 


.092837 


.071743 


.043001 


.025899 


.015672 


55 


.115656 


.088839 


.068326 


.040567 


.024204 


.014511 


56 


.111207 


.085013 


.065073 


.038271 


.022621 


.013436 


57 


.106930 


.081353 


.061974 


.036105 


.021141 


.012441 


58 


.102817 


.077849 


.059023 


.034061 


.019758 


.011519 


59 


.098863 


.074497 


.056212 


.032133 


.018465 


.010666 


60 


.095060 


.071289 


.053536 


.030314 


.017257 


.009876 


61 


.091404 


.068219 


.050986 


.028598 


.016128 


.009144 


62 


.087889 


.065281 


.048558 


.026980 


.015073 


.008467 


63 


.084508 


.062470 


.046246 


.025453 


.014087 


.007840 


64 


.081258 


.059780 


.044044 


.024012 


.013166 


.007259 


65 


.078133 


.057206 


.041946 


.022653 


.012304 


.006721 


66 


.075128 


.054743 


.039949 


.021370 


.011499 


.006223 


67 


.072238 


.052385 


.038047 


.020161 


.010747 


.005762 


68 


.069460 


.050129 


.036235 


.019020 


.010044 


.005336 


69 


.066788 


.047971 


.034509 


.017943 


.009387 


.004940 


70 


.064219 


.045905 


.032866 


.016927 


.008773 


.004574 


71 


.061749 


.043928 


.031301 


.015969 


.008199 


.004236 


72 


.059374 


.042037 


.029811 


.015065 


.007662 


.003922 


73 


.057091 


.040226 


.028391 


.014213 


.007161 


.003631 


74 


.054895 


.038494 


.027039 


.013408 


.006693 


.003362 


75 


.052784 


.036836 


.025752 


.012649 


.006255 


.003113 


76 


.050754 


.035250 


.024525 


.011933 


.005846 


.002883 


77 


.048801 


.033732 


.023357 


.011258 


.005463 


.002669 


78 


.046924 


.032280 


.022245 


.010620 


.005106 


.002471 


79 


.045120 


.030890 


.021186 


.010019 


.004772 


.002288 


80 


.043384 


.029559 


.020177 


.009452 


.004460 


.002119 


81 


.041716 


.028287 


.019216 


.008917 


.004168 


.001962 


82 


.040111 


.027069 


.018301 


.008412 


.003895 


.001817 


83 


.038569 


.025903 


.017430 


.007936 


.003640 


.001682 


84 


.037085 


.024787 


.016600 


.007487 


.003402 


.001557 


85 


.035659 


.023720 


.015809 


.007063 


.003180 


.001442 


86 


.034287 


.022699 


.015056 


.006663 


.002972 


.001335 


87 


.032969 


.021721 


.014339 


.006286 


.002777 


.001236 


88 


.031701 


.020786 


.013657 


.005930 


.002596 


.00114.5 


89 


.030481 


.019891 


.013006 


.005595 


.002426 


.001060 


90 


.029309 


.019034 


.012387 


.005278 


.002267 


.000981 


91 


.028182 


.018215 


.011797 


.004979 


.002119 


.000909 


92 


.027098 


.017430 


.011235 


.004697 


.001980 


.000841 


93 


.026056 


.016680 


.010700 


.004432 


.001851 


.000779 


94 


.025053 


.015961 


.010191 


.004181 


.001730 


.000721 


95 


.024090 


.015274 


.009705 


.003944 


.001616 


.000668 


96 


.023163 


.014616 


.009243 


.003721 


.001511 


.000618 


97 


.022272 


.013987 


.008803 


.003510 


.001412 


.000573 


98 


.021416 


.013385 


.008384 


.003312 


.001319 


.000530 


99 


.020592 


.012808 


.007985 


.003124 


.001233 


.000491 


100 


.019800 


.012257 


.007604 


.002947 


.001152 


.000455 



TABX.E XZZ. 

ANNUITIES CERTAIN-AMOUNTS, 

Showing the Amount of £1 per Annum forborn and improved for 
any number of years not exceeding 100. 



Years. 



1 
2 
3 
4 
5 

6 

7 

8 

9 

10 

11 
12 
13 
14 
15 

16 
17 

18 
19 
20 

21 

22 
23 
24 
25 

26 

27 
28 
29 
30 

31 
32 
33 
34 
35 

36 
37 
38 
39 
40 

41 
42 
43 
44 

45 

46 
47 
48 
49 
50 



1 W Cent. 



Cent, 



2 #" Cent, 121 ^ Cent. 3 <f Cent. 3^ f Cent 



1.000000 
2.010000 
3.030100 
4.060401 
5.101005 

6.152015 
7.213535 
8.285670 
9.368526 
10.462211 

11.566833 
12.682501 
13.809326 
14.947419 
16.096893 

17.257862 
18.430441 
19.614746 
20.810894 
22.019003 

23.239193 
24.471585 
25.716301 

26.973464 
28.243199 

29.525631 

30.820887 
32.129096 
33.450387 
34.784891 

36.132740 
37.494067 
38.869007 
40.257696 
41.660272 

43.076874 
44.507642 
45.952718 
47.412245 

48.886307 

50.375230 
51.878982 
53.397772 
54.931750 
5G.481068 

58.045879 
59.626338 
61.222602 
62.834829 
64.463178 



1 .000000 
2.015000 
3.045225 
4.090903 
5.152266 

6.229550 
7.322994 
8.432839 
9.559331 
10.702720 

11.863260 
13.041208 
14.236824 
15.450374 
16.682128 

17.932359 
19.201343 
20.489362 
21.796701 
23.123640 

24.470500 
25.837555 
27.225117 
28.633493 
30.062995 

i 31.513940 
32.986649 
34.481449 
35.998671 
37.538651 

39.101731 

40.688258 
42.298582 
43.933061 
45.592058 

47.275940 
48.985081 
50.719858 
52.480657 
54.267868 

56.081887 
57.923116 
59.791963 
61.688842 
63.614175 

65.568387 
67.551912 
69.565189 
71.608666 
73.682795 



1.000000 
2.020000 
3.060400 
4.121608 
5.204040 

6.308121 
7.434283 
8.582969 
9.754628 
10.949721 

12.168715 
13.412090 
14.680332 
15.973938 
17.293417 

18.639285 
20.012071 
21.412312 
22.840559 
24.297370 

25.783317 
27.298984 
28.844963 
30.421862 
32.030300 

33.670906 
35.344324 
37.051210 
38.792235 
40.568079 

42.379441 
44.227030 
46.111570 
48.033802 
49.994478 

51.994367 
54.034255 
56.114940 

58.237238 
60.401983 

62.610023 
64.862223 
67.159468 
69.502657 
71.892710 

74.330564 
76.817176 
79.353519 
81.940590 
84.579401 



1.000000 
2.025000 
3.075625 
4.152516 
5.256329 

6.387737 
7.547430 
8.736116 
9.954519 
11.203382 

12.483466 
13.795553 
15.140442 
16.518953 
17.931927 

19.380225 
20.864730 
22.386349 
23.946007 
25.544658 

27.183274 
28.862856 
30.584427 
32.349038 
34.157764 

36.011708 
37.912001 
39.859801 
41.856296 
43.902703 

46.000271 
48.150278 
50.354034 
52.612885 
54.928207 

57.301413 
59.733948 
62.227297 
64.782979 
67.402554 

70.087617 
72.839808 
75.660803 
78.552323 
81.516131 

84.554034 
87.667885 
90.859582 
94.131072 
97.484349 



1.000000 
2.030000 
3.090900 
4.183627 
5.309136 

6.468410 

7.662462 

8.892336 

10.159106 

11.463879 

12.807796 
14.192030 
15.617790 
17.086324 
18.598914 

20.156881 
21.761588 
23.414435 
25.116868 
26.870374 

28.676486 
30.536780 
32.452884 
34.426470 
36.459264 

38.553042 
[40.709634 
142.930923 
4.5.218850 
47.575416 

50.002678 
52.502759 
55.077841 
57.730177 
60.462082 

63.275944 
66.174223 
69.159449 
72.234233 
75.401260 

78.663298 
82.023196 
85.483892 
89.048409 
92.719861 

96.501457 
100.39650 
104.40840 
108.54065 
112.79687 



1.000000 
2.035000 
3.106225 
4.214943 
5.362466 

6.550152 

7.779408 

9.051687 

10.368496 

11.731393 

13.141992 
14.601962 
16.1130.30 
17.676986 
19.295681 

20.971030 
22.705016 
24.499691 
26.357181 

28.279682 

30.269471 
32.328902 
34.460414 
36.666528 

38.949857 

41.313102 
43.759060 
46.290627 
48.910799 
51.622677 

54.429471 
57.334.502 
60.341210 
63.453152 
66.674013 

70.007603 
73.457869 
77.028895 
80.724906 
84.550278 

88.509537 
92.607371 
96.848629 
101.23833 
105.78167 

110.48403 
115.35097 
120.38826 
125.60185 
130.99791 



TABXiS ZIZ. 

ANNUITIES CERTAIN— AMOUNTS, 

Showing the Amount of i'l per Annum forborn and improved for 
any number of years not exceeding 100. 



Years. 


4 ^ Cent. 


4^ f Cent. 


S^-Cent. 


6^ Cent. 


7 #" Cent. 


8 ^ Cent. 


1 


1.000000 


1.000000 


1.000000 


1.000000 


1.000000 


1 .000000 


2 


2.040000 


2.045000 


2.050000 


2.060000 


2.070000 


2.080000 


3 


3.121000 


3.137025 


3.152500 


3.183600 


3.214900 


3.246400 


4 


4.246464 


4.278191 


4.310125 


4.374016 


4.439943 


4.506112 


5 


5.416323 


5.470710 


5.525631 


5.G37093 


5.750739 


5.866601 


G 


6.632975 


6.716892 


6.801913 


C.975319 


7.153291 


7.335929 


7 


7.898294 


8.019152 


8.142008 


8.393838 


8.654021 


8.922803 


8 


9.214226 


9.380014 


9.549109 


9.897468 


10.259803 


10.636628 


9 


10.582795 


10.802114 


11.0265f)4 


11.491316 


11.977989 


12.487558 


10 


12.006107 


12.288209 


12.577893 


13.180795 


13.816448 


14.486562 


11 


13.486351 


13.841179 


14.206787 


14.971643 


15.783599 


16.645487 


12 


15.025805 


15.464032 


15.917127 


16.869941 


17.888451 


18.977126 


13 


16.626838 


17.159913 


17.712983 


18.882138 


20.140643 


21.495297 


14 


18.291911 


18.932109 


19.598632 


21.015066 


22.550488 


24.214920 


15 


20.023588 


20.784054 


21.578564 


23.275970 


25.129022 


27.152114 


16 


21.824531 


22.719337 


23.657492 


25.672528 


27.888054 


30.324283 


17 


23.697512 


24.741707 


25.840366 


28.212880 


30.840217 


33.750226 


18 


25.645413 


26.855084 


28.132385 


30.905653 


33.999033 


37.450244 


19 


27.671229 


29.063562 


30.539004 


33.759992 


37.378965 


41.446263 


20 


29.778079 


31.371423 


33.065954 


36.785591 


40.995492 


45.761964 


21 


31.969202 


33.783137 


35.719252 


39.992727 


44.865177 


50.422921 


22 


34.247970 


36.303378 


38.505214 


43.392290 


49.005739 


55.456755 


23 


36.617889 


38.937030 41.430475 


46.995828 


53.436141 


60.893296 


24 


39.082604 


41.689196144.501999 


50.815577 


58.176671 


66.764759 


25 


41.645908 


44.565210 


47.727099 


54.864512 


63.249038 


73.105940 


26 


44.311745 


47.570645 


51.113454 


59.156383 


68.676470 


79.954415 


27 


47.084214 


50.711324 


54.669126 


63.705766 


74.483823 


87.350768 


28 


49.967583 ' 


53.993333 


58.402583 


68.528112 


80.697691 


95.338830 


29 


52.966286 


57.423033 


62.322712 


73.639798 


87.346529 


103.96594 


30 


56.084938 


61.007070 


66.438848 


79.058186 


94.460786 


113.28321 


31 


59.328335 


64.752388 


70.760790 


84.801677 


102.07304 


123.34587 


32 


62.701469 


68.666245 


75.298829 


90.889778 


110.21815 


134.21354 


33 


66.209527 


72.756226 80.063771 


97.343165 


118.93343 


145.95062 


34 


69.857909 


77.030256 : 85.066959 


104.18376 


128.25877 


158.62667 


35 


73.652225 


81.496618! 90.320307 


111.43478 


138.23688 


172.31680 


36 


77.598314 


86.163966 


95.836323 


119.12087 


148.91346 


187.10215 


37 


81.702246 


91.041344 


101.62814 


127.26812 


160.33740 


203.07032 


38 


85.970336 


96.138205 


107.70955 


135.90421 


172.56102 


220.31595 


39 


90.409150 


101.46442 


114.09502 


145.05846 


185.64029 


2.38.94122 


40 


95.025516 


107.03032 


120.79977 


154.76197 


199.63511 


259.05652 


41 


99.826536 


112.84669 


127.83976 


165.04768 


214.60957 


280.78104 


42 


104.81960 


118.92479 


135.23175 


175.95055 


230.63224 


304.24352 


43 


110.01238 


125.27640 


142.99334 


187.50758 


247.77650 


329.58301 


44 


115.41288 


131.91384 


151.14301 


199.75803 


266.12085 


356.9496.5 


45 


121.02939 


138.84997 


159.70016 


212.74351 


285.74931 


386.50562 


46 


126.87057 


146.09821 


168.68516 


226.50812 


306.75176 


418.42607 


47 


132.94539 


153.07263 


178.11942 


241.09861 


329.22439 


452.90015 


48 


139.26321 


161.58790 


188.02539 


256.56453 


353.27009 


490.13216 


49 


145.83373 


169.85936 


198.42066 


272.95840 


378.99900 


530.34274 


50 


152.66708 


178.50303 '209.34800 


290.33590 


406.52893 


573.77016 



c z 



TABZiS III. 

, ANNUITIES CERTAIN— AMOUNTS, 

Showing the Amount of £1 per Annum forborn and improved for 
any number of years not exceeding 100. 



Years. 
51 


1 ^ Cent. 


lic^Cent. 


2 ^ Cent. 


2i ^ Cent. 


3 W Cent. 


3i ^ Cent. 


66.107810 


75.788035 


87.270989 


100.92146 


117.18077 


136.58284 


52 


67.768888 


77.924853 


90.016409 


104.44449 


121.69620 


142.36324 


53 


69.446577 


80.093723 


92.816737 


108.05561 


126.34708 


148.34595 


54 


71.141043 


82.295127 


95.673072 


111.75700 


131.13749 


154.53806 


55 


72.852454 


84.529552 


98.586534 


115.55092 


136.07162 


160.94689 


56 


74.580979 


86.797498 


101.55826 


119.43969 


141.15377 


167.58003 


57 


76.326789 


89.099462 


104.58943 


123.42569 


146.38838 


174.44533 


58 


78.090057 


91.435956 


107.68122 


127.51133 


151.78003 


181.55092 


69 


79.870958 


93.807497 


110.83484 


131.69911 


157.33343 


188.90520 


60 


81.669668 


96.214611 


114.05154 


135.99159 


163.05344 


196.51688 


61 


83.486365 


98.657831 


117.33257 


140.39138 


168.94504 


204.39497 


62 


85.321229 


101.13770 


120.67922 


144.90116 


175.01339 


212.54880 


63 


87.174442 


103.65477 


124.09281 


149.52369 


181.26379 


220.98801 


64 


89.046187 


106.20959 


127.57466 


154.26179 


187.70171 


229.72259 


65 


90.936649 


108.80273 


131.12616 


159.11833 


194.33276 


238.76288 


66 


92.846016 


111.43478 


134.74868 


164.09629 


201.16274 


248.11958 


67 


94.774477 


114.10630 


138.44365 


169.19870 


208.19762 


257.80376 


68 


96.722223 


116.81789 


142.21253 


174.42866 


215.44355 


267.82689 


69 


98.689446 


119.57016 


146.05678 


179.78938 


222.90686 


278.20084 


70 


100.67634 


122.36371 


149.97791 


185.28411 


230.59406 


288.93786 


71 


102.68311 


125.19916 


153.97747 


190.91622 


238.51189 


300.05069 


72 


104.70994 


128.07715 


158.05702 


196.68912 


246.66724 


311.55246 


73 


106.75704 


130.99831 


162.21816 


202.60635 


255.06726 


323.45680 


74 


108.82461 


133.96328 


166.46252 


208.67151 


263.71928 


335.77779 


75 


110.91286 


136.97273 


170.79177 


214.88830 


272.63086 


348.53001 


76 


113.02198 


140.02732 


175.20761 


221.26050 


281.80978 


361.72856 


77 


115.15220 


143.12773 


179.71176 


227.79202 


291.26407 


375.38906 


78 


117.30373 


146.27464 


184.30600 


234.48682 


301.00200 


389.52768 


79 


119.47676 


149.46876 


188.99212 


241.34899 


311.03206 


404.16115 


80 


121.67153 


152.71079 


193.77196 


248.38271 


321.36302 


419.30679 


81 


123.88825 


156.00145 


198.64740 


255.59228 


332.00391 


434.98252 


82 


126.12713 


159.34147 


203.62034 


262.98209 


342.96403 


451.20691 


83 


128.38840 


162.73159 


208.69275 


270.55664 


354.25295 


467.99915 


84 


130.67228 


166.17256 


213.86661 


278.32056 


365.88054 


485.37913 


85 


132.97901 


169.66514 


219.14394 


286.27857 


377.85695 


503.36739 


86 


135.30880 


173.21012 


224.52682 


294.43553 


390.19266 


521.98525 


87 


137.66188 


176.80827 


230.01735 


302.79642 


402.89844 


541.25474 


88 


140.03850 


180.46039 


235.61770 


311.36633 


415.98539 


561.19865 


89 


142.43889 


184.16730 


241.33006 


320.15049 


429.46496 


581.84061 


90 


144.86328 


187.92980 


247.15666 


329.15425 


443.34890 


603.20503 


91 


147.31191 


191.74875 


253.09979 


338.38311 


457.64937 


625.31720 


92 


149.78503 


195.62498 


259.16179 


347.84269 


472.37885 


648.20331 


93 


152.28288 


199.55936 


265.34502 


357.53875 


487.55022 


671.89042 


94 


154.80571 


203.55275 


271.65192 


367.47722 


503.17672 


696.40659 


95 


157.35376 


207.60604 


278.08496 


377.66415 


519.27203 


721.78082 


96 


159.92730 


211.72013 


284.64666 


388.10576 


535.85019 


748.04314 


97 


162.52657 


215.89593 


291.33959 


398.80840 


552.92569 


775.22465 


98 


165.15184 


220.13436 


298.16638 


409.77861 


570.51346 


803.35752 


99 


167.80335 


224.43638 


305.12971 


421.02308 


588.62887 


832.47503 


100 


170.48139 


228.80292 


312.23231 


432.54865 


607.28773 


862.61166 



TABXiB ZZZ. 

ANNUITIES CERTAIN— AMOUNTS, 

Showing the Amount of £1 per Annum forborn and improved for 
any number of years not exceeding 100. 



Years. 
51 


4 f Cent. 


4^ #• Cent. 


5 ^ Cent. 


6 ^ Cent. 


: 7 <^ Cent. 


8 #- Cent. 


159.77377 


187.53566 


220.81540 


308.75606 


435.98595 


620.67177 


52 


167.16472 


196.97477 


232.85617 


328.28142 


467.50497 


671.32551 


53 


174.85131 


206.83863 


245.49897 


348.97831 


501.23032 


726.03155 


54 


182.84536 


217.14637 


258.77392 


370.91701 


537.31644 


785.11408 


55 


191.15917 


227.91796 


272.71262 


394.17203 


575.92859 


848.92320 


56 


199.80554 


239.17427 


287.34825 


418.82235 


617.24359 


917.83706 


57 


208.79776 


250.93711 


302.71566 


444.95169 


661.45065 


992.26402 


58 


218.14967 


263.22928 


318.85144 


472.64879 


708.75219 


1072.6451 


59 


227.87566 


276.07460 


335.79402 


502.00772 


759.36484 


1159.4568 


60 


237.99069 


289.49795 


353.58372 


533.12818 


813.52038 


1253.2133 


61 


248.51031 


303.52536 


372.26290 


566.11587 


871.46681 


1354.4704 


62 


259.45073 


318.18400 


391.87605 


601.08282 


933.46949 


1463.8280 


63 


270.82875 


333.50228 


412.46985 


638.14779 


999.81235 


1581.9342 


64 


282.66190 


349.50989 


434.09334 


677.43666 


1070.7992 


1709.4890 


65 


294.96838 


366.23783 


456.79801 


719.08286 


1146.7552 


1847.2481 


66 


307.76712 


383.71853 


480.63791 


763.22783 


1228.0280 


1996.0279 


67 


321.07780 


401.98587 


505.66981 


810.02150 


1314.9900 


2156.7102 


68 


334.92091 


421.07523 


531.95330 


859.62279 


1408.0393 


2330.2470 


69 


349.31775 


441.02362 


559.55096 


912.20016 


1507.6020 


2517.6667 


70 


364.29046 


461.86968 


588.52851 


967.93217 


1614.1342 


2720.0801 


71 


379.86208 


483.65382 


618.95494 


1027.0081 


1728.1236 


2938.6865 


72 


396.05656 


506.41824 


650.90268 


1089.6286 


1850.0922 


3174.7814 


73 


412.89882 


530.20706 


684.44782 


1156.0063 


1980.5987 


3429.7639 


74 


430.41478 


555.06638 


719.67021 


1226.3667 


2120.2406 


3705.1450 


75 


448.63137 


581.04436 


756.65372 


1300.9487 


2269.6574 


4002.5566 


76 


467.57662 


608.19136 


795.48640 


1380.0056 


2429.5334 


4323.7612 


77 


487.27969 


636.55997 


836.26072 


1463.8059 


2600.6008 


4670.6620 


78 


507.77087 


666.20517 


879.07376 


1552.6343 


2783.6428 


5045.3150 


79 


529.08171 


697.18440 


924.02745 


1646.7924 


2979.4978 


5449.9402 


80 


551.24498 


729.55770 


971.22882 


1746.5999 


3189.0627 


5886.9354 


81 


574.29478 


763.38779 


1020.7903 


1852.3959 


3413.2971 


6358.8903 


82 


598.26657 


798.74025 


1072.8298 


1964.5396 


3653.2279 


6868.6015 


83 


623.19723 


835.68356 


1127.4713 


2083.4120 


3909.9538 


7419.0896 


84 


649.12512 


874.28932 


1184.8448 


2209.4167 


4184.6506 


8013.6168 


85 


676.09012 


914.63234 


1245.0871 


2342.9817 


4478.5761 


8655.7061 


86 


704.13373 


956.79079 


1308.3414 


2484.5606 


4793.0764 


9349.1626 


87 


733.29908 


1000.8464 


1374.7585 


2634.6343 


5129.5918 


10098.096 


88 


763.63104 


1046.8845 


1444.4964 


2793.7123 


5489.6632 


10906.943 


89 


795.17628 


1094.9943 


1517.7212 


2962.3351 


5874.9397 


11780.499 


90 


827.98333 


1145.2690 


1594.6073 


3141.0752 


6287.1854 


12723.939 


91 


862.10267 


1197.8061 


1675.3377 


3330.5397 


6728.2884 


13742.854 


92 


897.58677 


1252.7074 


1760.1045 


3531.3721 


7200.2686 


14843.282 


93 


934.49024 


1310.0792 


1849.1098 


3744.2544 


7705.2874 


16031.745 


94 


972.86985 


1370.0328 


1942.5653 


3969.9097 


8245.6575 


17315.284 


95 


1012.7846 


1432.6843 


2040.6935 


4209.1042 


8823.8535 


18701.507 


96 


1054.2960 


1498.1551 


2143.7282 


4462.6505 


9442.5233 


20198.627 


97 


1097.4679 


1566.5720 


2251.9146 


4731.4095 


10104.500 


21815.518 


98 


1142.3666 


1638.0678 


2365.5103 


5016.2941 


10812.815 


23501.759 


99 


1189.0613 ! 1712.7808 


2484.7859 


5318.2718 


11570.712 


25447.700 


100 


1237.6237 1790.8560 ' 2610.0252 ! 5638.3681 


12381.662 


27484.516 



TABZiB IV. 

ANNUITIES CERTAIN— PRESENT VALUES, 

Showing the Present Value of £1 per Annum for any number of 
years not exceeding 100. 



Years. 


l^Ceut. 


1 i #> Cent. 


2 ^ Cent. 


2i #■ Cent. 


3 #* Cent. 


3i#' Cent. 


1 


.990099 


.985222 


.980392 


.975610 


.970874 


.966184 


2 


1.970395 


1.955884 


1.941561 


1.927424 


1.913470 


1.899694 


3 


2.940985 


2.912201 


2.883883 


2.856024 


2.828611 


2.801637 


4 


3.901965 


3.854385 


3.807729 


3.761974 


3.717098 


3.673079 


5 


4.853431 


4.782645 


4.713460 


4.645828 


4,579707 


4.515052 


6 


5.795476 


5.697187 


5.601431 


5.508125 


5.417191 


5.328553 


7 


6.728194 


6.598214 


6.471991 


6.349391 


6.230283 


6.114544 


8 


7.651677 


7.485925 


7.325481 


7.170137 


7.019692 


6.873956 


9 


8.566017 


8.360517 


8.162237 


7.970866 


7.786109 


7.607687 


10 


9.471304 


9.222184 


8.982585 


8.752064 


8.530203 


8.316605 


11 


10.367628 


10.071117 


9.786848 


9.514209 


9.252624 


9.001551 


12 


11.255077 


10.907504 


10.575341 


10.257765 


9.954004 


9.663334 


13 


12.133739 


11.731531 


11.348374 


10.983185 


10.634955 


10.302738 


14 


13.003702 


12.543380 


12.106249 


11.690912 


11.296073 


10.920520 


15 


13.865051 


13.343232 


12.849264 


12.381378 


11.937935 


11.517411 


16 


14.717872 


14.131263 


13.577709 


13.055003 


12.561102 


12.094117 


17 


15.562249 


14.907648 


14.291872 


13.712198 


13.166118 


12.651321 


18 


16.398266 


15.672560 


14.992031 


14.353364 


13.753513 


13.189682 


19 


17.226006 


16.426167 


15.678462 


14.978891 14.323799 


13.709837 


20 


18.045550 


17.168638 


16.351433 


15.589162 


14.877475 


14.212403 


21 


18.856980 


17.900136 


17.011209 


16.184549 


15.415024 


14.697974 


22 


19.660376 


18.620823 


17.658048 


16.765413 


15.936917 


15.167125 


23 


20.455818 


19.330860 


18.292204 


17.332110 


16.443608 


15.620410 


24 


21.243384 


20.030404 


18.913926 


17.884986 


16.935542 


16.058368 


25 


22.023152 


20.719610 


19.523456 


18.424376 


17.413148 


16.481515 


26 


22.795200 


21.398630 


20.121036 


18.950611 


17.876842 


16.890352 


27 


23.559604 


22.067616 


20.706898 


19.464011 


18.327031 


17.285365 


28 


24.316440 


22.726715 


21.281272 


19.964889 


18.764108 


17.667019 


29 


25.065782 


23.376074 


21.844385 


20.453550 


19.188455 


18.035767 


30 


25.807705 


24.015836 


22.396456 


20.930293 19.600441 


18.392045 


31 


26.542282 


24.646144 


22.937702 


21.395407 


20.000428 


18.736276 


32 


27.269586 


25.267138 


23.468335 


21.849178 


20.388766 


19.068865 


33 


27.989689 


25.878954 


23.988564 


22.291881 


20.765792 


19.390208 


34 


28.702662 


26.481728 


24.498592 


22.723786 


21.131837 


19.700684 


35 


29.408576 


27.075594 


24.998619 


23.145157 


21.487220 


20.000661 


36 


30.107501 


27.660684 


25.488842 


23.556251 


21.832252 


20.290494 


37 


30.799506 


28.237127 


25.969453 


23.957318 22.167235 


20.570525 


38 


31.484659 


28.805051 


26.440641 


24.348603 22.492462 


20.841087 


39 


32.163029 


29.364582 


26.902589 


24.730344 22.808215 


21.102500 


40 


32.834682 


29.915844 


27.355479 


25.102775 23.114772 


21.355072 


41 


33.499685 


30.458960 


27.799489 


25.466122 23.412400 


21.599104 


42 


34.158104 


30.994049 


28.234794 


25.820607 23.701359 


21.834883 


43 


34.810004 


31.521231 


28.661562 


26.166446 23.981902 


22.062689 


44 


35.455449 


32.040622 


29.079963 


26.503849 24.254274 


22.282791 


45 


36.094504 


32.552337 


29.490160 


26.833024 24.518713 


22.495460 


46 


36.727232 


33.056490 


29.892314 


27.154170 24.775449 


22.700918 


47 


37.353695 


33.553192 


30.286582 


27.467483 25.024708 


22.899438 


48 


37.973955 


34.042554 


30.673120 


27.773154 25.266707 23.091244 1 


49 


38.588074 


34.524684 


31.052078 


28.071369 25.501657 


23.276564 


50 


39.196113 34.999689 


31.423606 


28.362312 25.729704 23.455618 j 



ANNUITIES CERTAIN— I'RESENT VALUES, 

Showing the Present Valve of £1 jjcr Annum for any number of 
years not exceeding 100. 



Years. 


4 f Cent. 


4i#'Cent. 


5 #* Cent. 


6<a^Cent. 


7 f Cent. 


8 #• Cent. 


1 


.961538 


.956938 


.952381 


.943396 


.934579 


.925926 


2 


1 .8800i)5 


1.872668 


1.859410 


1.833393 


1.808018 


1.783205 


3 


2.775091 


2.748964 


2.723248 


2.673012 


2.624316 


2.577097 


4 


3.629895 


3.587526 


3.545951 


3.4G5106 


3.387211 


3.312127 


5 


4.451822 


4.389977 


4.329477 


4.212364 


4.100197 


3.992710 


6 


5.242137 


5.157872 


5.075692 


4.917324 


4.766540 


4.622880 


7 


6.002055 


5.892701 


5.786373 


5.582381 


5.389289 


5.206370 


8 


6.732745 


6.595886 


6.463213 


6.209794 


5.971299 


5.746639 


9 


7.435332 


7.268790 


7.107822 


6.801692 


6.515232 


6.246888 


10 


8.110896 


7.912718 


7.721735 


7.360087 


7.023582 


0.710081 


11 


8.760477 


8.528917 


8.306414 


7.886875 


7.498674 


7.138964 


12 


9.385074 


9.118581 


8.863252 


8.383844 


7.942086 


7.530078 


13 


9.985648 


9.682852 


9.393573 


8.852683 


8.357051 


7.903770 


14 


10.563123 


10.222825 


9.898641 


9.294984 


8.745408 


8.244237 


15 


11.118387 


10.739546 


10.379658 


9.712249 


9.107914 


8.559479 


16 


11.652296 


11.234015 


10.837770 


10.105895 


9.446649 


8.851369 


17 


12.165669 


11.707191 


11.274066 


10.477260 


9.763223 


9.121638 


18 


12.659297 


12.159992 


11.689587 


10.827603 


10.059087 


9.371887 


19 


13.133939 


12.593294 


12.085321 


11.158116 


10.335595 


9.603599 


20 


13.590326 


13.007936 


12.462210 


11.469921 


10.594014 


9.818147 


21 


14.029160 


13.404724 


12.821153 


11.764077 


10.835527 


10.016803 


22 


14.451115 


13.784425 


13.163003 


12.041582 


11.061241 


10.200744 


23 


14.856842 


14.147775 


13.488574 


12.303379 


11.272187 


10.371059 


24 


15.246963 


14.495478 


13.798642 


12.550358 


11.469334 


10..528758 


25 


15.622080 


14.828209 


14.093945 


12.783356 


11.653583 


10.074770 


26 


15.982769 


15.146611 


14.375185 


13.003166 


11.825779 


10.809978 


27 


16.329586 


15.451303 


14.643034 


13.210534 


11.986709 


10.935165 


28 


16.663063 


15.742874 


14.898127 


13.406164 


12.1.37111 


11.051078 


29 


16.983715 


16.021889 


15.141074 


13.590721 


12.277674 


11.158406 


30 


17.292033 


16.288889 


15.372451 


13.764831 


12.409041 


11.257783 


31 


17.588494 


16.544391 


15.592811 


13.929086 


12.531814 


11.349799 


32 


17.873552 


16.788891 


15.802677 


14.084043 


12.646555 


11.434999 


33 


18.147646 


17.022862 


16.002.549 


14.2.30230 


12.753790 


11.513888 


34 


18.411198 


17.246758 


16.192904 


14..368141 


12.854009 


11.586934 


35 


18.664613 


17.461012 


16.374194 


14.498246 


12.947672 


11.054568 


30 


18.908282 


17.666041 


10.546852 


14.020987 


13.035208 


11.717193 


37 


19.142579 


17.862240 


16.711287 


14.730780 


13.117017 


11.775179 


38 


19.367864 


18.049990 


16.867893 


14.846019 


13.193473 


11.828869 


39 


19.584485 


18.229656 


17.017041 


14.949075 


13.264928 


11.878582 


40 


19.792774 


18.401584 


17.159086 


15.046297 


13.331709 


11.924613 


41 


19.993052 


18.566109 


17.294368 


15.138016 


13.394120 


11.9072.35 


42 


20.185627 


18.723550 


17.42.3208 


15.224.543 


13.452449 


12.006699 


43 


20.370795 


18.874210 


17.545912 


15.306173 


13.506962 


12.043240 


44 


20.548841 


19.018383 


17.662773 


15.383182 


13.557908 


12.077074 


45 


20.720040 


19.156347 


17.774070 


15.455832 


13.605522 


12.108402 


46 


20.884654 


19.288371 


17.880067 


15.524370 


13.650020 


12.137409 


47 


21.042936 


19.414709 


17.981016 


15.589028 


13.091608 


12.164267 


48 


21.195131 


19.535607 


18.077158 


15.650027 


13.730474 


12.189136 


49 


21.341472 


19.651298 


18.168722 


15.707572 


13.706799 


12.212103 


50 


21.482185 


19.762008 


18.255925 


15.761861 


13.800746 


12.233485 



TABZiB XV. 

ANNUITIES CERTAIN— PRESENT VALUES, 

Showing the Present Value of £1 per Annum for any number of 
years not exceeding 100. 



Years. 



51 
52 
53 
54 
55 

56 
57 
58 
59 
60 

61 
62 
63 
64 
65 

66 
67 
68 
69 
70 

71 

72 
73 
74 
75 

76 
77 
78 
79 
80 

81 
82 
83 
84 
85 

86 
87 
88 
89 
90 

91 
92 
93 
94 
95 

96 
97 
98 
99 
100 



Cent. 



Cent. 



Cent. 



2i ^ Cent. 



39.798132 
40.394190 
40.984346 
41.568659 
42.147187 

42.719987 
43.287116 
43.848630 
44.404584 
44.955034 

45.500034 
46.039638 
46.573899 
47.102870 
47.626604 

48.145152 
48.658566 
49.166897 
49.670195 
50.168510 

50.661891 
51.150387 
51.634046 
52.112917 

52.587047 

53.056482 
53.521269 
53.981454 
54.437083 
54.888201 

55.334852 
55.777081 
56.214932 
56.648448 
57.077671 

57.502644 
57.923410 
58.340010 
58.752485 
59.160876 

59.565224 
59.965568 
60.361948 
60.754404 
61.142974 

61.527697 
61.908611 
62.285753 
62.659161 

63.028872 



35.467674 
35.928743 
36.382998 
36.830540 
37.271468 

37.705880 
38.133872 
38.555533 
38.970968 
39.380264 

39.783511 
40.180799 
40.572216 
40.957848 
41.337781 

41.712099 
42.080886 
42.444223 
42.802190 
43.154867 

43.502332 
43.844662 
44.181933 
44.514220 
44.841596 

45.164134 
45.481905 
45.794980 
46.103429 
46.407319 

46.706718 
47.001693 
47.292309 
47.578630 
47.860719 

48.138639 
48.412452 
48.682219 
48.947999 
49.209851 

49.467834 
49.722004 
49.972418 
50.219131 
50.462198 

50.701673 
50.937609 
51.170058 
51.399072 
51.624701 



Perp. 1100.0000001 66.666067 



31.787849 
32.144950 
32.495049 
32.838283 
33.174788 

33.504694 
33.828131 
34.145227 
34.456104 
34.760887 

35.059693 
35.352640 
35.639843 
35.921415 
36.197466 

36.468104 
36.733435 
36.993564 
37.248592 
37.498619 

37.743744 
37.984063 
38.219670 
38.450657 
38.677114 

38.899132 
39.116796 
39.330192 
39.539404 
39.744514 

39.945602 
40.142747 
40.336026 
40.525516 
40.711290 

40.893422 
41.071982 
41.247041 
41.418668 
41.586929 

41.751891 
41.913619 
42.072175 
42.227623 
42.380023 

42.529434 
42.675916 
42.819525 
42.960319 
43.098352 



28.646158 
28.923081 
29.193250 
29.456829 
29.713979 

29.964858 
30.209617 
30.448407 
30.681373 
30.908656 

31.130397 
31.346728 
31.557784 
31.763691 
31.964577 

32.160563 
32.351769 
32.538311 
32.720303 

32.897857 

33.071080 
33.240078 
33.404954 
33.565809 
33.722740 

33.875844 
34.025214 
34.170940 
34.313113 
34.451817 

34.587139 
34.719160 
34.847961 
34.973620 
35.096215 

35.215819 
35.332507 
35.446348 
35.557413 
35.665768 

35.771481 
35.874616 
35.975235 
36.073400 
36.169171 

36.262606 
36.353762 
36.442694 
36.529458 
36.614105 



3 W Cent. 



25.951227 
26.166240 
26.374990 
26.577660 
26.774428 

26.965464 
27.150936 
27.331005 
27.505831 
27.675564 

27.840353 
28.000343 
28.155673 
28.306478 
28.452891 

28.595040 
28.733049 
28.867038 
28.997124 
29.123421 

29:246040 
29.365087 
29.480667 
29.592881 
29.701826 

29.807598 
29.910290 
30.009990 
30.106786 
30.200763 

30.292003 
30.380586 
30.466588 
30.550086 
30.631151 

30.709855 
30.786267 
30.860454 
30.932479 
31.002407 

31.070298 
31.136212 
31.200206 
31.262336 
31.322656 

31.381219 
31.438077 
31.493279 
31.546872 
31.598905 



3i #" Cent, 



23.628616 
23.795765 
23.957260 
24.113295 
24.264053 

24.409713 
24.550448 
24.686423 
24.817800 
24.944734 

25.067376 
25.185870 
25.300358 
25.410974 
25.517849 

25.621110 
25.720880 
25.817275 
25.910411 
26.000397 

26.087340 
26.171343 
26.252505 
26.330923 
26.406689 

26.479892 
26.550621 
26.618957 
26.684983 
26.748776 

26.810411 
26.869963 
26.927500 
26.983092 
27.036804 

27.088699 
27.138840 
27.187285 
27.234092 
27.279316 

27.323010 
27.365227 
27.406017 
27.445427 
27.483504 

27.520294 
27.555839 
27.590183 
27.623365 
27.655425 



50.000000 I 40.000000 | 33.333333 | 28.571429 



TABXfS ZV. 

ANNUITIES CERTAIN— PRESENT VALUES. 

Shewing the Present Value of £1 per Annum for any number of 
years not exceeding 100. 



Years. 4 ^ Cent. 



51 
52 
53 
54 
55 

56 

57 
58 
59 
60 

61 
62 
63 
64 
65 

66 
67 
68 
69 
70 

71 
72 
73 
74 
75 

76 
77 

78 
79 
80 

81 
82 
83 
84 
85 

86 
87 
88 
89 
90 

91 
92 
93 
94 
95 

96 
97 
98 
99 
100 



4i #* Cent. 



21.617485 
21.747582 i 
21.872675 
21.992957 
22.108612 

22.219819 
22.326749 
22.429567 
22.528430 
22.623490 

22.714894 
22.802783 
22.887291 
22.968549 
23.046682 

23.121810 
23.194048 
23.263507 
23.330296 
23.394515 

23.456264 
23.515639 
23.572730 
23.627625 
23.680408 

23.731162 
23.779963 
23.826888 
23.872008 
23.915392 

23.957108 
23.997219 
24.U35787 
24072872 
24.108531 

24.142818 
24.175787 
24.207487 
24.237969 
24.267278 

24.295459 
24.322557 
24..348612 
24.373666 
24.397756 

24.420919 
24.443191 
24.464607 
24.485199 
24.504999 



19.867950 
19.969330 
20.066345 
20.159181 
20.248021 

20.333034 
20.414387 
20.492236 
20.566733 
20.638022 

20.706241 
20.771523 
20.833993 
20.893773 
20.950979 

21.005722 
21.058107 
21.108236 
21.156207 
21.202112 



5 <^ Cent. 6 f Cent. 7 W Cent. 



,246040 
,288077 
,328303 
,366797 
.403634 

.438884 
.472616 
.504896 
.535785 
.565345 



21.593632 

21.620700 

21,646603 

21.671390. 

21.695110 

21.717809 
21.739530 
21.760316 
21.780207 
21.799241 

21.817455 
21.834885 
21.851565 
21.867526 
21.882800 

21.897417 
21.911403 
21.924788 
21.937596 
21.949853 



18.338977 
18.418073 
18.493403 
18.565146 
18.633472 

18.698545 
18.760519 
18.819542 
18.875754 
18.929290 

18.980276 
19.028834 
19.075080 
19.119124 
19.161070 

19.201019 
19.239066 
19.275301 
19.309810 
19.342677 

19.373978 
19.403788 
19.432179 
19.459218 
19.484970 

19.509495 
19.532853 
19.555098 
19.576284 
19.596460 

19.615677 
19.633978 
19.651407 
19.668007 
19.683816 

19.698873 
19.713212 
19.726869 
19.739875 
19.752262 

19.764059 
19.775294 
19.785994 
19.796185 
19.805891 

19.815134 16.604653 
19.823937 ' 16.608163 
19.832321 j. 16.611475 
19.840306 1 16.614599 
19.8479101 16.617546 



15.813076 
15.861393 
15.906974 
15.949976 
15.990543 

16.028814 
16.064919 
16.098980 
16.131113 
16.161428 

16.190026 
16.217006' 
16.242458 ; 
16.266470 
16.289123 1 

16.310493 
16.330654 
16.349673 
16.367617 
16.384544 

16.400513 
16.415578 
16.429791 
16.443199 
16.455848 

16.467781 
16.479039 
16.489659 
16.499679 
16.509131 

16.518048 

16.526460 

16.534396 

, 16.541883 

' 16.548947 

I 
16.555610 

16.561896 

16.567827 

16.573421 

16.578699 

16.583679 
16.588376 
16.592808 
16 596988 
1 16 600932 



8 ^' Cent. 



13.832473 
13.862124 
13.889836 
13.915735 
13.939939 

13.962560 
13.983701 
14.003459 
14.021924 
14.039181 

14.055309 
14.070383 
14.084470 
14.097635 
14.109940 

14.121439 
14.132186 
14.142230 
14.151617 
14.160389 

14.168588 
14.176251 
14.183412 
14.190104 
14.196359 

14.202205 
14.207668 
14.212774 
14.217546 
14.222005 

14.226173 
14.230069 
14.233709 
14.237111 
14.240291 I 

14.243262 ! 
14.246040 i 
14.248635 ; 
14.251061 ; 
14.253328 ' 

14.255447 | 
14.257427 
14.259277 \ 
14.261007 
14.262623 

14.264134 
14.265546 
14.266865 
14.268098 
14.269251 



Perp. 125.000000 1 22.222222 1 20.000000 1 16.666667 I 14.285714 



12.253227 
12.271506 
12.288432 
12.304103 
12.318614 

12.332050 
12.344491 
12.356010 
12.366676 
12.376552 

12.385696 
12..394163 
12.402003 
12.409262 
12.415983 

12.422207 
12.427969 
12.433.305 
12.438245 
12.442820 

12.447055 
12.450977 
12.454608 
12.457971 
12.461084 

12.463967 
12.466636 
12.469107 
12.471396 
12.473514 

12.475476 
12.477293 
12.478975 
12.480532 
12.481974 

12.483310 
12.484546 
12.485691 
12.486751 
' 12.487732 

I 12.488641 
12.489482 
; 12.490261 
: 12.490983 
1 12.491651 

■ 12.492269 
12.492842 
i 12.493372 
i 12.493863 
I 12.494318 

I 12.500000 1 



TABXiB V. 



NEW RATE OF MORTALITY. 

Exhibiting the Law of Mortality amongst Assured Lives according^ 
to the combined Town and Country Experience of Life Offices, deduced from 
62,537 Assurances under the superintendence of a Committee of eminent 
Actuaries.* 



Com- 


Number 


Deaths 


Logarithm of 


Com- 


Number 


Death? 


Logarithm of 


ploted 


Survivins; 

iit each 

Age. 


in each 


Number surviving 


pleted 


Surviving 

at each 

Age. 


in each 


Wimber surviving 


Age. 


Year. 


at each Age. 


Age. 


Year. 


at each Age. 


10 


100000 


676 


5.0000000 


55 


63469 


1375 


4.8025617 


11 


99324 


674 


4.9970542 


66 


62094 


1436 


4.7930496 


12 


98650 


672 


4.9940971 


57 


60658 


1497 


4.7828881 


13 


97978 


671 


4.9911286 


58 1 


59161 


1561 


4.7720355 


14 


97307 


671 


4.9881441 


59 


57600 


1627 


4.7604225 


15 


96636 


671 


4.9851389 


60 


55973 


1698 


4.7479786 


16 


95965 


672 


4.9821129 


61 


54275 


1770 


4.734599» 


17 


95293 


673 


4.9790610 


62 


52505 


1844 


4.7202007 


18 


94620 


675 


4.9759829 


63 


50661 


1917 


4.7046738 


19 


93945 


677 


49728737 


64 


48744 


1990 


4.6879212 


20 


93268 


680 


4.9697327 


65 


46754 


2061 


4.6098188 


21 


92588 


683 


4.9665547 


66 1 


44G93 


2128 


4.6502395 


22 


91905 


686 


4.9633391 


67 


42565 


2191 


4.6290526 


23 


91219 


690 


4.9600853 


68 


40374 


2246 


4.6061018 


24 


90529 


694 


4.9567877 


69 


38128 


2291 


4.5812440 


25 


89835 


698 


4.9534456 


70 


35837 


2327 


4.5543316 


26 


89137 


703 


4 9500580 


71 


33510 


2351 


4.5251744 


27 


88434 


708 


4 9466193 


72 


31159 


2362 


4.4935835 


28 


87726 


714 


4.9431283 


73 


28797 


2358 


4.4593472 


29 


87012 


720 


4.9395792 


' 74 


26439 


2339 


4.4222450 


30 
31 


8G292 


727 


4.9359705 


1 75 


24100 


2303 


4.3820170 


85565 


734 


4.P322962 


76 


21797 


2249 


4.3383967 


32 


84831 


742 


4.9285546 


77 


19548 


2179 


4.2911023 


33 


84089 


750 


4.9247392 


78 


17369 


2092 


4.2397748 


34 


83339 


758 


4.9208483 


79 


15277 


1987 


, 4.1840381 


35 


82581 


767 


4.9168801 


80 


13290 


1806 


1 4.1235250 


36 


81814 


776 


4.9128276 


81 


11424 


1730 


4.0578182 


37 


81038 


785 


4.9086887 


82 


9694 


1582 


3.9865030 


38 


80253 


795 


4.9044613 


83 


8112 


1427 


3.9091279 


39 


79458 


805 


4.9001376 


84 


6685 


1268 


3.8251014 


40 


78653 


815 


4.8957153 


85 


5417 


1111 


3.7337588 


41 


77838 


826 


4.8911917 


86 


4306 


958 


3.6340740 


42 


77012 


839 


4.8865584 


87 


3348 


811 


3.5247854 


43 


76173 


857 


4.8818011 


88 


2537 


673 


3.4043205 


44 


75316 


881 


4.8768872 


89 


1864 


545 


3.2704459 


45 


. 74435 


909 


4.8717772 


90 


1319 


427 


3.1202448 


46 


73526 


944 


4.8664409 


91 


892 


322 


2.9503649 


47 


72582 


981 


4.8608289 


92 


570 


231 


2.7558749 


48 


71601 


1021 


4.8549191 


93 


339 


155 


2.5301997 


49 


! 70580 

j 


1063 


4.8486817 


94 


184 


95 


2.2048178 


50 


69517 


1108 


4.8420910 


95 


89 


52 


1.9493900 


51 


68409 


1156 


4.83511.32 


96 


37 


24 


1.5682017 


52 


67253 


1207 


4.8277117 


97 


13 


9 


1.1139434 


53 


66046 


1201 


4.8198465 


98 


i 4 


3 


0.6020600 


54 


64785 


1316 


4.8114745 


99 


i 1 


1 


0.0000000 



• Messrs. Charles Ansell of the "Atlas;" Griffith Davies of the "Guardian;" J.J.Downes 
of the "Economic;" Benjamin Gompertz of the ''Alliance;" George Kirkpatrick of the 
"LawLife;" JoshuaMilne of the "Sun;" J. M. Rainbow of the "Crown;" W. S. B. Wol- 
house of the "National Loan Fund," and Samuel Ingall, of the "Imperial," Secretary to the 
Committee. 



TABLE VZ. 



PROBABILITIES OF LIFE. 

Shewing the Probability of Dying: in one Year, the Probability of 
Surviving One Year, and the Logarithm of the Probability of Sur- 
viving One Year. (Deduced from Table V.) 



Com- 


Proba- 
bility of 
Dying in 
one year. 


Probability 


Loparilhm 
of Proba- 


Com- 


.?,7? 'f Probability 

^^\'y of OfSurviving 

J^J'"S '" one year, 
one year. ' 


Logarithm 
of I'roba- 


pleted 
Age. 


ofSurviving 
one year. 


bility of 
Surviving 


pleted 
Age. 


biliiyof 
Surviving 


10 






one year. 
9.9970542 




.0216643 




one year. 


.0067600 


.9932400 


55 


.9783357 


9.9904879 


11 


.0067859 


.9932141 


9.9970429! 


56 


.0231261 .9768739 


9.9898385 


12 


.0068119 


.9931881 


9.9970315 


57 


.0240793 1 .9753207 


9.9801474 


13 


.0008484 


.9931516 


9.9970155 


58 


.0263856 .9736 144 


9 9883870 


14 


.0068959 


.9931041 


9.9969948 1 


59 


.0282464 


.9717536 


9.9875561 


15 


.0069434 


.9930566 


9.9969740 1 


60 


.0303362 


,9696638 


9.9866212 


16 


.0070026 


.9929974 


9.9969481 \ 


61 


.03261161.9673884 


9.9856009 


17 


.00706251.9929375 


9.9969219; 


62 


.03512041.9648796 


9.9844731 


18 


.0071336 


.9928664 


9.9968908! 


63 


.0378398 1.9621602 


9.9832474 


19 


.0072064 


.9927936 


9.9968590; 


64 


.0408256 .9591744 


9.9818976 


20 


.0072909 


.9927091 


9.9968220 


65 


.0440818 .9559182 


9.9804207 


21 


.0073768 


.9926232 


9.9967844 


66 


.0476138 .9523862 


9.9788131 


22 


.0074641 


.9925359 


9.9967462 


67 


.0514741 .9485259 


9 9770492 


23 


.0075643 


.9924357 


9.9967024 


68 


.0556300 .9443700 


9.9751422 


24 


.0076659 


.9923341 


9.9966579 


i 69 


.0600872 


.9399128 


9.9730876 


25 


.0077700 


.9922300 


9.9966124 


1 70 


.0649328 


.9350672 


9.9708428 


23 


.0078866 '.9921134 


9.9965613 


71 


.0701581 


.9298419! 9.9684091 


27 


.0080061 ,.9919939 


9.9965090 


72 


.0758049 


.9241951 19.9657637 


23 


.0081389 '.9918611 


9.9964509' 


73 


.0818834 


.9181166 9.9628978 


29 


.0082750 .9917250 


9.9963913 


74 


.0884679 


.9115321 


9.9597720 


30 


.0084248 


.9915752 


9.9963257 


75 


.0955602 


.9044398 


9.9563797 


31 


.0085784 


.9914216 


9.9962584 


76 


.1031794 


.8968206 


9.9527056 


32 


.0087468 


.9912532 


9.9961846 


77 


.1114692 


.8885308 


9 9486725 


33 


.0089191 .9910-09 


9.2961091 


78 


.1204444 


.8795556 9.9442633 


34 


.0090955 1 .9909045 


9.9960318 


79 


.1300648 


.8699352 9.9394869 


35 


.0092877 .9907123 


9.9959475 


80 


.1404064 


.8595936 9.9342932 


36 


.0094849 .9905151 


9.9958611 


81 


.1514357 


.8485643 9.9286848 


37 


.0096867 ' .9903133 


99957726 


82 


.1631938 


8368062 9.9226249 


38 


.0099064 i .9900936 


9.9956763 


83 


.1759121 


.8240879 9.9159735 


39 


.0101311!. 9898689 

I 


9.9955777 


84 


.1896785 


.8103215 


9.9086574 


40 


.0103619 .9896381 


9.9954764 


85 


.2050951 


.7949049 9.9003152 


41 


.0106118 .9893882 


9.9953667 


86 


.2224804 


.7775196 9.8907114 


42 


.0108943 .9891057 


9.9952427 


87 


.2422340 


.7577660 9.8795351 


43 


.0112509 .9887491 


9.9950861 


88 


.2652741 


.7347259 9.8661254 


44 


.0116973 .9883027 


9.9948900 


89 


.2923820 


.7076180 9.8497989 

i 


45 


.0122120 .9877880 


9.9946637 


90 


.3237300 


.6762700 9.8301201 


46 


.01283891.9671611 


9.9943880 


91 


.3609866 


.6390134 9.8055100 


47 


.01351571.9864843 


9.9940902 


92 


.405-2632 


.5947368 9.7743248 


48 


.0142595 '.9857405 


9.9937626 


93 


.4572271 


.5427729 9.7346181 


49 


.01506111.9849389 


9.9934093 


94 


.5163043 


.4836957 9.6845722 


50 


.0159386 .9840614 


9.9930222 


95 


.5842697 


.414730319.6188117 


51 


.0168982;. 9831 018 


9.99-25985 


96 


.6486486 


.3513514 9.5457417 


52 


.0179473 .9820527 


9.9921348 


97 


.6923077 


.3076923 9.4881166 


53 


.0190927 .9809073 


9.9916280 


98 


.7500000 


.2500000 9.3979400 


54 


.0203133 


.9796867 


9.991d^72 


99 


1.000000 


.0000000 ; 



TABZ.S VIZ. 

EXPECTATION OF LIFE. 

Shewing the Expectation of Life at every Age 
according to the Law of Mortality amongst Assured 
Lives. (Deduced from Table V.) 



Completed 


Expectation 


Completed 


Expectation 


Age. 


of Life. 


Age. 


of Life. 


10 


48.36 


55 


16.86 


11 


47.68 


56 


16.22 


12 


47.01 


57 


15.59 


13 


46.33 


58 


14.97 


14 


45.64 


59 


14.37 


15 


44.96 


60 


13.77 


16 


44.27 


61 


13.18 


17 


43.58 


62 


12.61 


18 


42.88 


63 


12.05 


19 


42.19 


64 


11.51 


20 


41.49 


65 


10.97 


21 


40.79 


66 


10.46 


22 


40.09 


67 


9.96 


23 


39.39 


68 


9.47 


24 


38.68 


69 


9.00 


25 


37.98 


70 


8.54 


26 


37.27 


71 


8.10 


27 


36.56 


72 


7.67 


28 


35.86 


73 


7.26 


29 


35.15 


74 


6.86 


30 


34.43 


75 


6.48 


31 


33.72 


76 


6.11 


32 


33.01 


77 


5.76 


33 


32.30 


78 


5.42 


34 


31.58 


79 


5.09 


35 


30.87 


80 


4.78 


36 


30.15 


81 


4.48 


37 


29.44 


82 


4.18 


38 


28.72 


83 


3.90 


39 


28.00 


84 


3.63 


40 


27.28 


85 


3.36 


41 


26.56 


86 


3.10 


42 


25.84 


87 


2.84 


43 


25.12 


88 


2.59 


44 


24.40 


89 


2.35 


45 


23.69 


90 


2.11 


46 


22.97 


91 


1.89 


47 


22.27 


92 


1.67 


48 


21.56 


93 


1.47 


49 


20.87 


94 


1.28 


50 


20.18 


95 


1.12 


51 


19.50 


96 


.99 


52 


18.82 


97 


.89 


53 


18.16 


98 . 


.75 


54 


17.50 


99 


.50 



TABXiS VXXZ. 



COMPARATIVE EXPECTATIONS OF LIFE. 

Shewing the Expectation or Average duration of Life deduced from Eight 
Original Tables prepared under the Superintendence of a Committee of eminent 
Actuaries, and compared with the Carlisle, Equitable, and Northampton Tables. 





Male 


Female 
























Lives- 
Town, 
Coun- 
try and 


Lives- 
Town, 
Coun- 
try and 


Town 
Expe- 
rience. 


Coun- 
try 
Expe- 


Irish 
Expe- 
rience. 


Com- 
bined 
Town 
Expe- 
rience. 


Gene- 
ral 
Expe- 


Ad- 
justed 
Expe- 
rience. 


Car- 
lisle 
Expe- 


Equi- 
table 
Expe- 


North 
amp- 
tan 
Expe- 
rience 


at* 


o 
O 


Irish 
Expe- 


Irish 
Expe- 




rience. 




rience. 


(Table 
7.) 


rience. 


rience. 


o 
O 




rience, 


rience. 








41.55 






41.46 






20 


20 


39.84 


85.86 


41.22 


40.83 


34.95 


40.97 


41.49 


41.06 


33.43 


21 


39.29 


86.01 


40.68 


40.29 


.34.48 


40.96 


40.45 


40.79 


40.75 


40.33 


32.90 


21 


22 


38.70 


86.20 


40.47 


39.89 


33.48 


40.38 


89.92 


40.09 


40.04 


39.60 


32.39 


22 


23 


37.98 


85.41 


39.87 


88.98 


32.78 


39.65 


39.18 


39.39 


39-31 


38.88 


31.88 


23 


24 


37.41 


84.81 


89.28 


88.37 


32.64 


38.98 


88.54 


88,68 


38.59 


38.16 


31.36 


24 


25 


36.63 


84.41 


88.56 


87.55 


31.94 


88-26 


87.84 


37.98 


37.86 


37.44 


30.85 


25 


26 


35.88 


83.79 


87.82 


36.88 


31.05 


37.54 


37.13 


37.27 


37.14 


36.78 


30.33 


26 


27 


35.23 


38.14 


37.10 


36.12 


30.99 


86.81 


86.42 


.36.56 


36.41 


36.02 


29.82 


27 


28 


34.63 


83.07 


86.45 


85.54 


30.76 


36.12 


35.76 


35.86 


35.69 


35.33 


29.30 


28 


29 


33.96 


82.61 


85.67 


84.91 


30.56 


85.38 


35.06 


35.15 


85.00 


34.65 


28.79 


29 


30 


33.17 


81.73 


34.84 


34.20 


29.71 


34.54 


34-25 


34.43 


34.34 


33.98 


28.27 


30 


31 


32.44 


31.04 


34.07 


33.51 


29.08 


83.78 


33.50 


33.72 


33.68 


33.30 


27.76 


31 


32 


81.73 


80.51 


3334 


32.86 


28.36 


.33.01 


32.75 


33.01 


38.03 


32.64 


27.24 


32 


33 


30.92 


29.86 


82.53 


32.05 


27.63 


32.22 


31.98 


32.30 


32.36 


31.98 


26-72 


33 


34 


30.21 


29.60 


31-87 


31.41 


26.85 


81.51 


.'31.27 


31.58 


3L68 


31.32 


26.20 


34 


35 


29.52 


29.07 


31.12 


30.78 


26.30 


30.77 


80.55 


30.87 


31.00 


30.66 


25.68 


35 


36 


28.87 


28.88 


30.44 


30.20 


25.77 


30.08 


29.90 


30.15 


80..82 


30.01 


25.16 


36 


37 


28.15 


28.30 


2969 


29.45 


25.26 


29.37 


29.20 


29.44 


29.64 


29.35 


24.64 


37 


88 


27.49 


27.62 


29.00 


28.81 


24.61 


28.65 


28.51 


28.72 


28.96 


28.70 


24.12 


38 


89 


26.81 


27.00 


28.34 


28.16 


28.93 


27.92 


27.79 


28.00 


28.28 


28.05 


23.60 


89 


40 


26.06 


26-36 


27-53 


27.38 


23-36 


27,20 


27.07 


27.28 


27-61 


27.40 


23.08 


40 


41 


25.42 


25.84 


26-85 


26.73 


22.86 


26.51 


26.41 


26.56 


26.97 


26.74 


22.56 


41 


42 


24.70 


•25.34 


26-19 


26.01 


22.14 


25.79 


25.68 


25.84 


26.84 


26.07 


22.04 


42 


43 


24.00 


24.57 


25.47 


25.22 


21.56 


25.07 


24.98 


25.12 


25.71 


25.40 


21.54 


43 


44 


23.34 


23.94 


24.77 


24.59 


21.00 


24.32 


24.26 


24.40 


25.09 


24.75 


21.03 


44 


45 


22.63 


23.21 


24.08 


23.83 


20.30 


23.61 


23.55 


2369 


24.46 


24.10 


20.52 


45 


46 


21.98 


22.60 


2342 


23.13 


19.76 


22.90 


22.85 


22.97 


23.82 


23.44 


20.02 


46 


47 


21.24 


21.97 


22.70 


22.34 


19.12 


22.15 


22.12 


22.27 


23.17 


22.78 


19.51 


47 


48 


20.62 


21.16 


22.01 


21.67 


18.59 


21.44 


21.41 


21.56 


22.50 


22.12 


19.00 


48 


49 


20.08 


20.69 


21.34 


21.13 


18.27 


20.77 


20.79 


20.87 


21.81 


21.47 


18.49 


49 


60 


19.41 


20.05 


20.58 


20.48 


17.76 


20.07 


20.11 


20.18 


21.11 


20.83 


17.99 


50 


51 


18-73 


19.46 


19.89 


19.73 


17.20 


19.41 


19.46 


19.50 


20.39 


20.20 


17..50 


51 


52 


18.05 


18.80 


19.17 


19 03 


16.62 


18,75 


18.79 


18.82 


19-68 


19.59 


17.02 


52 


53 


17-40 


18.31 


18.52 


18.30 


16.11 


18.11 


18.16 


18.16 


18.97 


19.00 


16.54 


53 


54 


16-77 


17.58 


17.95 


17.55 


15.51 


17.46 


17.50 


17.50 


18.28 


18.43 


16.06 


54 


55 


16.21 


16.78 


17.25 


16.96 


15.04 


16,76 


1683 


16.86 


17.58 


17.85 


15.58 


55 


56 


15.66 


16.07 


16.74 


16.40 


14.41 


16,17 


16.23 


16.22 


16.89 


17.28 


15.10 


56 


57 


15.09 


15.39 


16.08 


15.87 


13.85 


15,56 


15,62 


15.59 


16.21 


16.71 


14.63 


57 


58 


14-45 


14.79 


15.85 


15.24 


13.34 


14.90 


14,98 


14.97 


15.55 


16.15 


14.15 


58 


59 


13-99 


14.28 


14.86 


14.60 


13.04 


14,25 


14.38 


14.37 


14.92 


15.60 


13.68 


59 


60 


13.47 


18.78 


14.23 


14.03 


12.67 


13.68 


13.81 


13.77 


14.34 


15.06 


13.21 


60 


61 


12.99 


13.10 


13.58 


13.50 


12.29 


13.08 


13.24 


18.18 


13,82 


14.51 


12.75 


61 


62 


12.46 


12.41 


13.01 


12.87 


11.81 


12 52 


12.68 


12.61 


13.31 


13.96 


12.28 


62 


63 


11.90 


11.87 


12.26 


12.26 


11.45 


11.91 


12.09 


12.05 


12.81 


13.42 


11.81 


63 


64 


11.27 


11.09 


11.62 


11.75 


10.67 


11.32 


11.50 


11.51 


12.30 


12.88 


11.35 


64 


65 


10.87 


10.60 


11.18 


11.44 


10.19 


10.86 


11.03 


10.97 


11.79 


12.35 


10.88 


65 


66 


10.38 


10-00 


10.69 


10.82 


9.74 


10.37 


10.51 


10.46 


11.27 


11.83 


10.42 


66 


67 


9.93 


9.56 


10.11 


10.26 


9.44 


9.87 


10.03 


9.96 


10.75 


11.32 


9.96 


67 


68 


9-33 


8-85 


9.57 


9.72 


8.73 


9.S1 


9.46 


9,47 


10.23 


10.82 


9.50 


68 


69 


8.81 


8.38 


9.29 


8.94 


8.27 


8,88 


8.99 


9.00 


9.70 


10.32 


9.05 


69 


70 


8.34 


7.98 


8.61 


8.48 


7.92 


844 


8.50 


8.54 


9,18 


9.84 


8.60 


70 


71 


7-88 


7.31 


8.33 


7.92 


7.37 


8.10 


8.13 


8.10 


8.65 


9.36 


8,17 


71 


72 


7.43 


6.63 


7.65 


7.37 


6.98 


7.69 


7.72 


7.67 


8,16 


8.88 


7,74 


72 


73 


6.97 


6.19 


7.08 


6.76 


6.70 


7.22 


7.26 


7.26 


7,72 


8.42 


7,83 


73 


74 


6.57 


5.72 


6.53 


6.81 


6.37 


6.79 


6.84 


6.86 


7.33 


7.97 


6.92 


74 


75 


6.03 


5.37 


6-29 


5.55 


5.97 


6.45 


6.46 


6.48 


7-01 


7.52 


6.54 


75 


76 


5.63 


5.45 


6.34 


5.45 


5.34 


6.10 


6.08 


6.11 


6-69 


7.08 


6.18 


76 


77 


5.48 


4.78 


5.52 


4.90 


5.59 


6.74 


5.77 


5.76 


6-40 


6.64 


5.83 


77 


78 


5.16 


4.56 


5.19 


4.69 


5.23 


5.32 


5.37 


5.42 


6.12 


6.20 


6.48 


78 


79 


4.99 


4.80 


5.82 


4.91 


4.80 


6.05 


5.07 


5.09 


5.80 


6.78 


5.11 


79 


80 


4.75 


4.75 


4.76 


4.75 


4.76 


4.75 


475 


4.78 


5.51 


5.3S 


4.75 


80 



TABXjB 2X. 

LIFE ANNUITIES AND ASSURANCES- 



SINGLE LIVES. 



Preparatory Table for determining the values of Annuities and As- 
surances for the whole term of Life, or for temporary and deferred 
periods, according to the combined experience of various Life Offices. 

(21 PER CENT.) 



Age 


D 


N 


S 


M 


R 


10 


78119.840 2 


017796.413 


43023298.36 


26999.930 


995447.53 


11 


75699.268 1 


942097.145 


41005501.95 


26484.720 


968447.00 


12 


73351.788 1 


868745.357 


39063404.80 


25983.563 


941962.88 


13 


71075.238 1 


797670.119 


37194659.45 


25496.081 


915979.32 


14 


68866.811 1 


728803.308 


35396989.33 


25021.196 


890483.24 


15 


66723.830 1 


662079.478 


33668186.02 


24557.894 


865462.04 


16 


64644.416 1 


597435.062 


32006106.54 


24105.891 


840904.15 


17 


62626.089 1 


534808.973 


30408671.48 


23664.256 


816798.26 


18 


60667.118 1 


474141.855 


28873862.51 


23232.751 


793134.00 


19 


58765.202 1 


415376.653 


27399720.65 


22810.520 


769901.25 


20 


56918.750 1 


358457.903 


25984344.00 


22397.367 


747090.73 


21 


55125.625 1 


303332.278 


24625886.10 


21992.504 


724693.36 


22 


53384.367 1 


249947.911 


23322553.82 


21595.774 


702700.86 


23 


51693.555 1 


198254.356 


22072605.91 


21207.019 


681 105.08 


24 


50051.252 1 


148203.104 


20874351.55 


20825.535 


659898.07 


25 


48456.153 1 


099746.951 


19726148.45 


20451.198 


639072.53 


26 


469116.984 1 


052839.967 


18626401.50 


20083.886 


618621.33 


27 


45401.991 1 


007437.976 


17573561.53 


19722.966 


598537.45 


28 


43940.002 


963497.974 


16566123.55 


19368.345 


578814.48 


29 


42519.392 


920978.582 


15602625.58 


19019.441 


559446.13 


30 


41139.080 


879839.502 


14681647.00 


18676.186 


540426.69 


31 


39797.549 


840041.953 


13801807.50 


18338.048 


521750.50 


32 


38493.809 


801548,144 


12961765.54 


18004.980 


503412.46 


33 


37226.450 


764321.694 


12160217.40 


17676.494 


485407.48 


34 


35994.559 


728327.135 


11395895.70 


17352.565 


467730.99 


35 


34797.245 


693529.890 


10667568.57 


17033.166 


45037842 


36 


33633.221 


659896.669 


9974038.68 


16717.857 


433345.25 


37 


32.501.671 


627394.998 


9314142.011 


16406.629 


416627.40 


38 


31401.789 


595993.209 


8686747.013 


16099.470 


400220.77 


39 


30332.407 


565660.802 


8090753.804 


15795.986 


384121.30 


40 


29292.785 


536368.017 


7525093.002 


15496.179 


368325.31 


41 


28282.199 


508085.818 


6988724.985 


15200.052 


352829.13 


42 


27299.586 


480786.232 


6480639.167 


14907.247 


337629 08 


43 


26343.583 


454442.649 


5999852.935 


14617.088 


322721.83 


44 


25411.901 


429030.748 


5545410.286 


14327.933 


308104.75 


45 


24502.096 


404528.652 


5116379.538 


14037.931 


293776.81 


46 


23612.563 


380916.089 


4711850.886 


13746.009 


279738.88 


47 


22740.880 


358175.209 


4330934.797 


13450.242 


265992.87 


48 


21886.361 


336288.848 


3972759.588 


13150.378 


252542.63 


49 


21048.068 


315240.780 


3636470.740 


12845.900 


239392.25 


50 


20225.429 


295015.351 


3321229.960 


12536.629 


226546.35 


51 


19417.625 


275597.726 


3026214.609 


12222.127 


214009.72 


52 


18623.901 


256973.825 


2750616.883 


11902.004 


201787.60 


53 


17843.565 


239130.260 


2493643.058 


11575.911 


189885.59 


64 


17075.983 


222054.277 


2254512.798 


11243.537 


178309.68 



V or 

LIFE ANNUITIES AND ASSURANCES— SINGLE LIVES. 

Prepai-atory Table for determining the values of Annuities and As- 
surances for the whole term of Lite, or for temporary and deferred 
periods, according to the combined experience of various Life Offices. 

(•2.3 PER CENT.) 



Age. 


D 


1 
N 


S 


M 


R 


55 


16321.086 


205733.191 


2032458.521 1 


10905.127 


167066.15 


56 


15578.052 


19015.5.139 j 


1826725.330 


10560.169 i 


156161.02 


57 


14846.625 ; 


175308.514 


1636570.191 


10208.694 ; 


145600.85 


58 


14127.044 


101181.470 


1401261.677 


9851.2260 


135392.16 


59 


13418.823 


147762.647 i 


1300080.207 , 


9487.5666 


12c 540.93 


60 


12721.745 i 


135040.902 


1152317.560 


9117.7762 


116053.36 


61 


12034.944 1 


123005.958 


1017276.658 


8741.2616 


106935.59 


62 1 


11358.501 ' 


111647.4.57 


894270.700 


8358.3544 


98194.325 


63 1 


10692.278 


100955.179 


78-2623.243 


7969.1683 


89835.971 


64 


10036.765 


90918.414 


681668.064 


7574.4433 


81866.803 


65 


9392.203 


81526.211 


590749.650 


7174.6810 


74292.350 


66 


8759.199 


72767.012 


509223.439 


6770.7540 


67117.678 


67 


8138.674 


64628.338 


436456,427 


6363.8681 


60346.924 


68 


7531.456 


57096.882 


371828.089 


5955.1541 


53983.056 


69 


6939.006 


50157.876 


314731.207 


5546.3992 


48027.902 


70 


6362.987 


43794.889 


264573.331 


5139.6239 


42481.503 


71 


5804.703 


37990.186 


220778.442 


4736.5340 


37341.879 


72 


5265.810 


32724.376 


182788.2.56 


4.339.2196 


32605.345 


73 


4747.937 


27976439 


150063.880 


3949.7823 


28266.125 


74 


4252.839 


23723.600 


122087.441 


3570.4868 


24316.343 


75 


3782.049 


19941.551 


98363 841 


3203.4240 


20745.856 


76 


33.37.205 


16604.346 


78422.290 


2850.8258 


17542.4.32 


77 


2919.878 


13084.468 


61817.944 


2514.8935 


14691.007 


78 


2531.123 


11153.345 


48133.476 


2197.3555 


12176.713 


79 


2171.964 


8981.381 


36980.131 


1899.9313 


9979.358 


80 


1843.384 


7137.997 


27998.750 


1624.3254 


8079.426 


81 


1545.913 


5592.084 


20860.753 


1371.8155 


6455.101 


82 


1279.812 


4312.272 


15268.669 


1143.4192 


5083.285 


83 


1044.833 


3267.4392 


10956.3972 


939.6561 


3939.866 


84 


840.0336 


2427.4056 


7688.9580 


760.3400 


3000.210 


85 


664.0951 


1763.3105 


5261.5524 


604.8901 


2239.870 


86 


515.0171 


1248.2934 


3498.2419 


472.0095 


1634.980 


87 


390.6691 


857.6243 


2249.9485 


360.2230 


1162.970 


88 


288.8154 


568.8089 


' 1392.3242 


267.8977 


802.7475 


89 


207.0245 


361.7844 


823.5153 


193.1512 


534.8498 


90 


142.9213 


218.86312 


461.73086 


134.0973 


341.6986 


91 


94.29596 


124.56716 


242.86774 


88.95783 


207.6014 


92 


58.78672 


65.78044 


! 118.30058 


55.74849 


118.6435 


93 


34.10988 


31.67056 


52..52014 


32.50548 


62.8951 


94 


18.06236 


13.60820 


i 20.84958 

1 


17.28990 


30.3896 


95 


8.52359 


1 5.08461 


7.24138 


8.19168 


13.0997 


96 


3.45709 


1 162752 


! 2.15677 


3.33.307 


4.90799 


97 


1.18503 


i 0.44249 


0.52925 


1.145331 


1.57492 


98 


0.35573 


1 0.08676 


0.08676 


0.344938 


0.42958 


99 


0.08676 


0.00000 


0.00000 


0.084647 


0.08465 



TABXiE X. 

LIFE ANNUITIES AND ASSURANCES- 



SINGLE LIVES. 



Preparatory Table for determining the values of Annuities and As- 
surances, for the whole term of Life, or for temporary and deferred 
periods, according to the combined experience of various Life Offices. 

(3 PER CENT.) 



Age. 


D 


N 


S 


M 


R 


10 


74409.391 


1737895.587 


34875249.57 


21623.808 


743735.36 


11 


71753.769 


1666141.818 


33137353.98 


21135.452 


722111.55 


12 


69191.125 


1596950.693 


31471212.16 


20662.722 


700976.10 


13 


66718.250 


1530232.443 


29874261.47 


20205.122 


680313.37 


14 


64331.391 


1465901.052 


28344029.03 


19761.512 


660108.25 


15 


62026.971 


1403874.081 


26878127.98 


19330.823 


640346.74 


16 


59802.215 


1344071.866 


25474253.90 


18912.678 


621016.92 


17 


57653.833 


1286418.033 


24130182.03 


18506.107 


602103.24 


18 


65579.278 


1230838.755 


22843764.00 


18110.790 


683597.13 


19 


53575.521 


1177263.234 


21612925.25 


17725.847 


565486.34 


20 


51640.230 


1125623.004 


20435662.02 


17351.009 


547760.50 


21 


49770.613 


1075852.391 


19310039.02 


16985.475 


630409.49 


22 


47964.530 


1027887.861 


18234186.63 


16629.022 


613424.01 


23 


46219.915 


981667.946 


17206298.77 


16281.432 


496794.99 


24 


44534.270 


937133.676 


16224630.82 


15941.998 


480513.66 


25 


42905.695 


894227.981 


15287497.14 


15610.539 


464671.56 


26 


41332.357 


852895.624 


14393269.16 


15286.880 


448961.02 


27 


39812.019 


813083.605 


13540373.54 


14970.398 


433674.14 


28 


38342.995 


774740.610 


127272e9.93 


14660.947 


418703.74 


29 


36923.226 


737817.384 


11952549.32 


14357.964 


404042.80 


30 


35551.161 


702266.223 


11214731.94 


14061.333 


389684.83 


31 


34224.900 


668041.323 


10512465.72 


13770.543 


376623.50 


32 


32943.018 


635098.305 


9844424.394 


13485.503 


361862.96 


33 


31703.760 


603394.545 


9209326.089 


13205.750 


348367.46 


34 


30505.816 


572888.729 


8605931.544 


12931.216 


335161.70 


35 


29347.917 


543540.812 


8033042.815 


12661.835 


322230.49 


36 


28228.483 


615312.329 


7489502.003 


12397.196 


309568.65 


37 


27146.347 


488165.982 


6974189.674 


12137.249 


297171.46 


38 


26100.374 


462065.608 


6486023.692 


11881.946 


285034.21 


39 


25089.146 


436976.462 


6023958.084 


11630.922 


273162.26 


40 


24111.615 


412864.847 


6586981.622 


11384.144 


261521.34 


41 


23166.768 


389698.079 


5174116.775 


11141.577 


250137.19 


42 


22253.327 


367444.752 


4784418.696 


10902.897 


238995.62 


43 


21369.797 


346074.955 


4416973.944 


10667.521 


228092.72 


44 


20513.953 


325561.002 


4070898.989 


10434.099 


217425.20 


45 


19683.489 


305877.513 


3745337.987 


10201.128 


206991.10 


46 


18876.809 


287000.704 


3439460.474 


9967.7548 


196789.97 


47 


18091.700 1 


268909.004 


3152459.770 


9732.4545 


186822.22 


48 


17327.356 


251581.648 


2883550.766 


9495.0537 


177089.76 


49 


16582.791 


234998.857 


2631969.118 


9266.1695 


167594.71 


50 


15857.320 


219141.537 


2396970.261 


9012.6917 


168339.64 


51 


15150.075 


203991.462 


2177828.724 


8767.3105 


149326.86 


52 


14460.256 


189531.206 


1973837.262 


8518.7657 


140669.54 


53 


13787.122 


175744.084 


1784306.056 


8266.7941 


132040.78 


54 

1 


13129.988 


162614.096 


1608561.972 


8011.2270 


123773.99 



LIFE ANNUITIES AND ASSURANCES-SINGLE LIVES. 

Preparatory Table for determining the values of Annuities and As- 
surances, for the \vhole term of Life, or for temporary and deferred 
periods, accordino^ to the combined experience of various Life Offices, 

(3 PER CENT.) 



Years. 


D 


N 

1 


S 


M 


11 


55 


12488.615 


[150125.481 


1445947.876 


7752.2815 


115762.76 


56 


11862.195 


1138263.286 


1295822..395 


7489.6060 


108010.48 


57 


11250.356 


127012.930 


1157559.109 


7223.2693 


100520.87 


58 


10653.112 


116359.8179 


1030546.179 


6053.7048 


93297.003 


59 


10069.9246 


106289.8933 


914186.361 


6680.8029 


86343.898 


60 


9500.4702 


96789.4231 


807896.468 


6404.6472 


79663.095 


61 


8943.9451 


87845.4780 


711107.045 


6124.8348 


73258.448 


62 


8400.2602 


79445.2178 


623261.567 


5841.6530 


67133.613 


63 


7869.1640 


71576.0538 


543816.349 


5555.2249 


61291.960 


64 


7350.8705 


64225.1833 


472240.295 


5266.1305 


55736.735 


65 


6845.4050 


57379.7783 


408015.112 


4974.7681 


50470.605 


66 


6353.0557 


51026.7226 


350635.334 


4681.7995 


45495.837 


67 


5874.3331 


45152.3895 


299608.611 


4388.1174 


40814.037 


68 


5409.6665 


39742.7230 


254456.222 


4094.5478 


36425.920 


69 


4959.9295 


34782.7935 


214713.499 


3802.3741 


32331.372 


70 


4526.1183 


30256.6752 


179930.706 


3513.0269 


28528.998 


71 


4108.9560 


26147.7192 


149674.031 


3227.6930 


25015.971 


72 


3709.3972 


22438.3220 


123526.312 


2947.8127 


21788.278 


73 


3328.3564 


19109.9656 


101087.990 


2674.8128 


18840.465 


74 


2966.8145 


16143.1511 


81978.024 


2410.2132 


16165.652 


75 


2625.5795 


13517.5716 


65834.873 


2155.3903 


13755.439 


76 


2305.5134 


11212.0582 


52317.301 


1911.7973 


11600.049 


77 


2007.4097 


9204.6485 


41105.2426 


1680.8446 


9688.2516 


78 


1731 .6945 


7472.9540 


31900.5941 


1463.5977 


8007.4070 


79 


1478,7588 


5994.1952 


24427.6401 


1261.0997 


6543.8093 


80 


1248.9556 


4745.23959 


18433.4449 


1074.3672 


5282.7096 


81 


1042.3246 


3702.91499 


13688.2053 


904.1136 


4208.3424 


82 


858.71807 


2844.19692 


9985.2903 


750.8660 


3304.2288 


83 


697.65114 


2146.54578 


7141.0934 


614.8103 


2553.3628 


84 


558.18032 


1588.36546 


4994.5476 


495.6595 


1938.5525 


85 


439.13164 


1149.23382 


3406.1821 


392.8685 


1442.8930 


86 


338.90088 


810.33294 


2256.9483 


305.42803 


1050.0245 


87 


255.82730 


554.50564 


1446.6154 


232.22536 


744.5965 


88 


188.21086 


366.29478 


892.1098 


172.06020 


512.3711 


89 


134.25576 


232.03902 


525.8150 


123.58696 


340.3109 


90 


92.23475 


139.80427 


293.7760 


85.47631 


216.7239 


91 


60.55882 


79.24545 


153.9717 ' 


56.48683 


131.2476 


92 


37.57077 


41.07468 


74.72624 


35.26264 


74.76080 


93 


21.69390 


19.98078 


33.05156 


20.48007 


39.49816 


94 


11.43190 


8.54888 


13.07078; 


10.84993 


19.01809 


95 


5.36850 


3.18038 


4.52190 


5.11950 


8.16816 


96 


2.16684 


1.01354 


1.34152 i 


2.07420 


3.04806 


97 


0.73915 


0.27439 


0.32798 


0.70962 


0.97446 


98 


0.22080 


0.05359 


0.05359 


0.21281 


0.26484 


99 1 


0.05359 


0.00000 


0.00000 


0.0520 3 


0.05203 



LIFE ANNUITIES AND ASSURANCES- 



SINGLE LIVES. 



Preparatory Table for determining the values of Annuities and As- 
surances for the whole term of Life, or for temporary and deferred 
periods, according to the combined experience of various Life Offices. 

(3i PER CENT.) 





Age. 


D 


N 


S 


M 


R 




10 


70891.881 


1506695.178 


27483798.21 


17543.524 


561018.40 




11 


68031.548 


1438663.630 


25977103.03 


17080.501 


543474.87 




12 


65284.922 


1373378.708 


24538439.40 


16634.459 


526394.37 




13 


62647.540 


1310731.168 


23165060.69 


16204.779 


509759.91 




14 


60114.491 


1250616.677 


21854329.52 


15790.248 


493555.13 




16 


57681.122 


1192935.555 


20603712.84 


15389.734 


477764.89 




16 


55343.582 


1137591.973 


19410777.28 


15002.764 


462375.15 




17 


53097.620 


1084494.353 


18273185.31 


14628.324 


447372.39 




18 


50939.731 


1033554.622 


17188690.96 


14266.007 


432744.06 




19 


48866.026 


984688.596 


16155136.34 


13914.901 


418478.06 




20 


46873.313 


937815.283 


15170447.74 


13574.664 


404563.16 




21 


44958.039 


892857.244 


14232632.46 


13244.476 


390988.49 




22 


43117.289 


849739.955 


13339775.21 


12924.046 


377744.02 




23 


41348.262 


808391.693 


13490035.26 


12613.092 


364819.97 




24 


39647.821 


768743.872 


12681643.57 


12310.902 


352206.88 




25 


38013.408 


730730.464 


11912899.69 


12017.238 


339895.98 




26 


36442.563 


694287.901 


11182169.23 


11731.869 


327878.74 




27 


34932.512 


659355.389 


10487881.33 


11454.176 


316146.87 




28 


33481.008 


625874.381 


9828525.940 


11183.964 


304692.69 




29 


32085.513 


593788.868 


9202651.559 


10920.678 


293508.73 




30 


30743.976 


563044.892 


8608862.691 


10664.158 


282588.05 




31 


29454.070 


533590.822 


8045817.799 


10413.902 


271923.89 




32 


28213.917 


505376.905 


7512226.977 


10169.781 


261509.99 




33 


27021.387 


478355.518 


7006850.072 


9931.3450 


251340.21 




34 


25874.763 


452480.755 


6528494.554 


9698.4880 


241408.86 




35 


24772.389 


427708.366 


6076013.799 


9471.1055 


231710.38 




36 


23712.374 


403995.992 


56483P5.433 


9248.8038 


222239.27 




37 


22693.202 


381302.790 


5244309.441 


9031.4993 


212990.47 




38 


21713.407 


359589.383 


4863006.651 


8819.1082 


203958.97 




39 


20771.315 


338818.068 


4503417.268 


8611.2853 


195139.86 




40 


19865.580 


318952.488 


4164599.200 


8407.9645 


186528.57 




41 


18994.913 


299957.575 


3845646.712 


8209.0789 


178120.61 




42 


18157.820 


281799.755 


3545689.137 


8014.3254 


169911.53 




43 


17352.658 


264447.097 


3263889.382 


7823.1962 


161897.20 




44 


16577.227 


247869.870 


2999442.285 


7634.5685 


154074.01 




45 


15829.291 


232040.579 


2751572.415 


7447.2157 


146439.44 




46 


15107.229 


216933.350 


2519531.836 


7260.4454 


138992.22 




47 


14408.955 


202524.395 


2302598.486 


7073.0428 


131731.78 




48 


13733.534 


188790.861 


2100074.091 


6884.8807 


124658.74 




49 


13079.903 


175710.958 


1911283.230 


6695.6688 


117773.86 




50 


12447.253 


163263.705 


1735572.272 


6505.3351 


111078.19 




51 


11834.648 


151429.057 


1572308.567 


6313.6529 


104572.85 




52 


11241.219 


140187.838 


1420879.510 


6120.4296 


98259.198 




53 


10666.156 


129521.682 


1280691.672 


5925.5042 


92138.769 




54 


10108.704 


119412.978 


1151169.990 


5728.7445 


86213.264 



TABLB XZ. 

LIFE ANNUITIES AND ASSUKANCES— SINGLE LIVES. 

Preparatory Table for determining the values of Annuities and As- 
surances for the whole term of Life, or for temporary and deferred 
periods, according to the combined experience of various Life Offices. 

(31 PER CENT.) 



Age. 


D 


N 


S 


:\i 


R 


55 


9568.466 


109844.512 


1031757.012 


5530.3468 


80484..520 


56 


9044.613 


100799.899 


92191 2..500 


5330.0643 


74954.173 


57 


8536.663 


92263.236 


821112.601 


5127.9699 


69624.109 


58 


8044.429 


84218.807 


728849.365 


4924.4150 


64496.1.30 


59 


7567.316 


76651.491 


644630.558 


4719.3355 


59571.724 


60 


7104.894 


69546.597 


567979.067 


4512.8134 


54852.388 


61 


6656.385 


62890.212 


498432.470 


4304.5676 


50339.575 


62 


6221.555 


56668.657 


4.35542.258 


4094.8323 


460.35.007 


63 


5800.049 


50868.608 


378873.601 


3883.7174 


41940.175 


64 


5391.860 


45476.748 


328004.993 


3671.6667 


38056.458 


65 


4996.846 


40479.902 


282528.245 


3458.9849 


34384.791 


66 


4615.050 


35864.852 


242048.343 


3246.1637 


30925.806 


67 


4246.677 


31618.175 


206183.491 


3033.8549 


27679.642 


68 


3891.866 


27726.309 


174565.316 


2822.6526 


24645.788 


69 


3551.075 


24175.234 


146839.007 


2613.4700 


21823.1.35 


70 


3224.832 


20950.402 


122663.773 


2407.3118 


19209.665 


71 


2913.463 


18036.939 


101713.371 


2204.9052 


16802.353 


72 


2617.449 


15419.490 


83676.4.32 


2007.5041 


14597.358 


73 


2337.229 


13082.261 


68256.942 


1815.7987 


12589.854 


74 


2073.285 


11008.976 


55174.681 


1630.8898 


10774.055 


75 


1825.959 


9183.017 


44165.705 


1453.6734 


9143.16.53 


76 


1595.621 


7587.396 


34982.688 


1285.0851 


7689.4919 


77 


1382.596 


6204.800 


27395.292 


1126.0173 


6404.4068 


78 


1186.937 


5017.863 


21190.492 


977.1121 


5278.3895 


79 


1008.672 


4009.191 


16172.629 


838.9866 


4.301.2774 


80 


847.806 


3161.385 


12163.438 


712.2303 


3462.2908 


81 


704.125 


2457.260 


9002.0527 


597,2182 


2750.0605 


82 


577.2904 


1879.9697 


6544.7926 


494.1945 


2152.8423 


83 


466.7443 


1413.2254 


4664.8229 


40.3.1702 


1658.6478 


84 


371.6310 


1041.5944 


3251.5975 


323.8407 


1255.4776 


85 


290.9572 


750.6372 


2210.0031 


255.7341 


931.6369 


86 


223.4621 


527.1751 


1459.3659 


198.0782 


675.9028 


87 


167.8707 


359.3044 


932.1908 


150.0435 


477.8246 


88 


122.9051 


236.39934 


572.8864 


110.7546 


327.7810 


89 


87.24784 


149.15150 


336.48707 


79.25367 


217.0264 


90 


59.65039 


89.50111 


187.33557 


54.60661 


137.7727 


91 


38.97561 


50.52550 


97.83446 


35.94900 


83.16612 


92 


24.06371 


26.46179 


47.30896 


22.35512 


47.21712 


93 


13.82760 


12.63419 


20.84717 


12.93277 


24.86200 


94 


7.25145 


5.38274 


8.21298 


6.82421 


11.92923 


95 


3.38888 


1.99386 


2.83024 


3.20686 


5.10502 


96 


1.36122 


0.63264 


0.83638 


1.29379 


1.89816 


97 


0.46209 


0.17055 


0.20374 


0.44070 


0.60437 


98 


0.13737 


0.03318 


0.03318 


0.13161 


0.16367 


99 

1 


0.03318 


0.00000 


0.00000 


0.03206 


0.03206 







TABX.E XIX. 








LIFE ANNUITIES— SINGLE LIVES. 




Shewing the Values of Annuities on Single Lives according to the 


combined experience 


of various Life Offices. 






Age. 


2 f Cent. 


2| W Cent. 


3^ Cent. 


3i W Cent. 


4 f Cent. 


10 


28.762 


25.832 


23.356 


21.253 


19.454 


11 


28.537 


25.658 


23.220 


21.147 


19.369 


12 


28.306 


25.479 


23.080 


21.036 


19.282 


13 


28.070 


25.295 


22.936 


20.922 


19.191 


14 


27.829 


25.106 


22.787 


20.804 


19.096 


15 


27.583 


24.912 


22.633 


20.682 


18.998 


16 


27.331 


24.713 


22.475 


20.555 


18.896 


17 


27.074 


24.509 


22.313 


20.424 


18.790 


18 


26.812 


24.300 


22.146 


20.290 


18.681 


19 


26.545 


24.086 


21.974 


20.151 


18.567 


20 


26.272 


23.867 


21.797 


20.007 


18.451 


21 


25.995 


23.643 


21.616 


19.860 


18.329 


22 


25.712 


23.414 


21.430 


19.708 


18.204 


23 


25.423 


23.180 


21.239 


19.551 


18.075 


24 


25.129 


22.941 


21.043 


19.389 


17.941 


25 


24.830 


22.696 


20.842 


19.223 


17.803 


26 


24.525 


22.446 


20.635 


19.052 


17.660 


27 


24.214 


22.190 


20.423 


18.875 


17.512 


28 


23.898 


21.928 


20.205 


18.693 


17.360 


29 


23.576 


21.661 


19.982 


18.506 


17.202 


30 


23.248 


21.388 


19.754 


18.314 


17.040 


31 


22.914 


21.109 


1L.519 


18.116 


16.872 


32 


22.575 


20.824 


19.279 


17.912 


16.698 


33 


22.230 


20.533 


19.032 


17.703 


16.520 


34 


21.878 


20.236 


18.780 


17.487 


16.335 


35 


21.521 


19.932 


18.521 


17.265 


16.144 


36 


21.157 


19.622 


18.255 


17.037 


15.948 


37 


20.787 


19.305 


17.983 


16.802 


15.744 


38 


20.410 


18.981 


17.703 


16.561 


15.534 


39 


20.026 


18.650 


17.417 


16.312 


15.317 


40 


19.636 


18.312 


17.123 


16.055 


15.093 


41 


19.238 


17.966 


16.821 


15.791 


14.861 


42 


18.833 


17.613 


16.512 


15.519 


14.621 


43 


18.422 


17.252 


16.195 


15.240 


14.374 


44 


18.004 


16.885 


15.870 


14.952 


14.119 


45 


17.581 


16.512 


15.540 


14.658 


13.857 


46 


17.155 


16.134 


15.204 


14.360 


13.590 


47 


16.725 


15.752 


14.864 


14.055 


13.317 


48 


16.294 


15.367 


14.519 


13.747 


13.039 


49 


15.860 


14.979 


14.171 


13.434 


12.757 


50 


15.424 


14.588 


13.820 


13.116 


12.470 


51 


14.988 


14.195 


13.465 


12.795 


12.179 


52 


14.550 


13.800 


13.107 


12.471 


11.884 


53 


14.112 


13.403 


12.747 


12.143 


11.585 


54 


13.675 


13.005 


12.385 


11.813 


11.283 



TABXiB XZZ. 

LIFE ANNUITIES— SINGLE LIVES. 

Shewing the Values of Annuities on Single Lives accordino- to the 
combined experience of various Life Offices. " 



Age. 


41 ^ Cent. 


5 ^ Cent. 


6 ^ Cent. 


7 4f Cent. 


8 #" Cent. 


10 


17.902 


16.556 


14..347 


12.625 


11.251 


11 


17.835 


16.502 


14.312 


12.601 


11.234 


12 


17.765 


16.445 


14.274 


12.575 


11.210 


13 


17.692 


16.386 


14.234 


12.547 


11.196 


14 


17.616 


16.324 


14.193 


12.518 


11.175 


15 


17.536 


16.259 


14.149 


12.487 


11.153 


16 


17.453 


16.192 


14.102 


12.454 


11.129 


17 


17.367 


16.121 


14.054 


12.420 


11.104 


18 


17.278 


16.048 


14.003 


12.384 


11.078 


19 


17.185 


15.971 


13.950 


12.346 


11.050 


20 


17.089 


15.891 


13.894 


12.306 


11.021 


21 


16.989 


15.808 


13.836 


12.264 


10.990 


22 


16.885 


15.722 


13.775 


12.220 


10.957 


23 


16.778 


15.632 


13.712 


12.174 


10.923 


24 


16.666 


15.539 


13.645 


12.125 


10.887 


25 


16.551 


15.442 


13.576 


12.074 


10.849 


26 


16.431 


15.341 


13.503 


12.020 


10.809 


27 


16.307 


15.236 


13.427 


11.964 


10.767 


28 


16.178 


15.127 


13.347 


11.905 


10.722 


29 


16.045 


15.014 


13.264 


11.843 


10.675 


30 


15.907 


14.896 


13.177 


11.778 


10.625 


31 


15.764 


14.774 


13.087 


11.710 


10.573 


32 


15.616 


14.647 


12.992 


11.638 


10.518 


33 


15.463 


14.515 


12.893 


11.563 


10.460 


34 


15.304 


14.378 


12.789 


11.484 


10.398 


35 


15.139 


14.2.35 


12.681 


11.401 


10.333 


36 


14.969 


14.087 


12.568 


11.313 


10.264 


37 


14.792 


13.933 


12.450 


11.221 


10.191 


38 


14.609 


13.773 


12.326 


11.124 


10.114 


39 


14.419 


13.606 


12.196 


11.022 


10.032 


40 


14.223 


13.433 


12.060 


10.914 


9.945 


41 


14.018 


13.252 


11.918 


10.800 


9.853 


42 


13.806 


13.064 


11.768 


10.680 


9.755 


43 


13.586 


12.868 


11.612 


10.553 


9.652 


44 


13.359 


12.666 


11.448 


10.420 


9.543 


45 


13.126 


12.456 


11.279 


10.281 


9.428 


46 


12.886 


12.241 


11.104 


10.137 


9.308 


47 


12.641 


12.020 


10.923 


9.988 


9.182 


48 


12.391 


11.794 


10.737 


9.833 


9.053 


49 


12.135 


11.563 


10.546 


9.074 


8.918 


50 


11.875 


11.326 


10.349 


9.509 


8.779 


51 


11.611 


11.085 


10.148 


9.338 


8.635 


52 


11.342 


10.840 


9.942 


9.164 


8.486 


53 


11.069 


10.590 


9.731 


8.985 


8.332 


54 

1 


10.792 


10.336 


9.515 


8.801 


8.174 



TABIiX: XIX. 

LIFE ANNUITIES-SINGLE LIVES. 

Shewing the Values of Annuities on Single Lives according to the 
combined experience of various Life Offices. 



Age. 


2 c^ Cent. 


2i#'Cent. 


3 W Cent. 


3i W Cent. 


4#'Cent. 1 


55 


13.238 


12.606 


12.021 


11.480 


10.978 


56 


12.801 


12.207 


11.656 


11.145 


10.670 


57 


12.366 


11.808 


11.290 


10.808 


10.359 


58 


11.933 


11.409 


10.923 


10.469 


10.046 


59 


11.501 


11.011 


10.555 


10.129 


9.731 


60 


11.072 


10.614 


10.188 


9.788 


9.415 


61 


10.647 


10.220 


9.822 


9.448 


9.098 


62 


10.226 


9.829 


9.457 


9.108 


8.780 


63 


9.810 


9.441 


9.096 


8.770 


8.464 


64 


9.400 


9.058 


8.737 


8.434 


8.149 


65 


8.996 


8.680 


8.382 


8.101 


7.835 


66 


8.599 


8.307 


8.032 


7.771 


7.525 


67 


8.210 


7.941 


7.686 


7.445 


7.217 


68 


7.828 


7.581 


7.347 


7.124 


6.913 


69 


7.455 


7.228 


7.013 


6.808 


6.613 


70 


7.091 


6.883 


6.685 


6.497 


6.317 


71 


6.735 


6.545 


6.364 


6.191 


6.026 


72 


6.388 


6.214 


6.049 


6.891 


6.740 


73 


6.050 


5.892 


5.742 


6.597 


5.459 


74 


5.721 


5.578 


5.441 


5.310 


5.184 


75 


5.402 


5.273 


5.148 


5.029 


4.915 


76 


5.09i.\ 


4.975 


4.863 


4.755 


4.651 


77 


4.792 


4.687 


4.585 


4.488 


4.394 


78 


4.501 


4.406 


4.315 


4.228 


4.143 


79 


4.220 


4.135 


4.053 


3.975 


3.899 


80 


3.947 


3.872 


3.799 


3.729 


3.661 


81 


3.684 


3.617 


3.553 


3.490 


3.429 


82 


3.428 


3.369 


3.312 


3.256 


3.203 


83 


3.179 


3.127 


3.077 


3.028 


2.980 


84 


2.935 


2.890 


2.846 


2.803 


2.761 


85 


2.694 


2.655 


2.617 


2.580 


2.544 


86 


2.457 


2.424 


2.391 


2.359 


2.328 


87 


2.223 


2.195 


2.167 


2.140 


2.114 


88 


1.992 


1.969 


1.946 


1.923 


1.901 


89 


1.766 


1.747 


1.728 


1.709 


1.691 


90 


1.545 


1.531 


1.516 


1.500 


1.485 


91 


1.331 


1.321 


1.309 


1.296 


1.284 


92 


1.129 


1.119 


1.109 


1.100 


1.090 


93 


0.936 


0.928 


0.921 


0.914 


0.906 


94 


0.759 


0.753 


0.748 


0.742 


0.737 


95 


0.601 


0.596 


0.592 


0.588 


0.584 


96 


0.474 


0.471 


0.468 


0.465 


0.462 


97 


0.376 


0.373 


0.371 


0.369 


0.367 


98 


0.245 


0.244 


0.243 


0.242 


0.240 


99 













TABLE XII. 

LIFE ANNUITIES-SINGLE LIVES. 

Shewing the Values of Annuities on Single Lives according to the 
combined experience of various Life Offices. 



Age. 


4i #" Cent. 


j 5 #^ Cent. 


6 ^ Cent. 


7 ^ Cent. 


8 #• Cent. 


55 


10.512 


10.077 


i 9.295 


8.612 


8.011 


56 


10.228 


9.816 


; 9.071 


8.419 


7.844 


57 


9.941 


9.550 


8.843 


8.221 


7.672 


58 


9.651 


9.282 


8.611 


8.019 


7.495 


59 


9.359 


9.010 


i 8.375 

1 


7.813 


7.314 


60 


9.064 


8.735 


8.136 


7.603 


7.129 


61 


8.769 


8.459 


7.893 


7.390 


6.940 


62 


8.472 


8.182 


7.649 


7.174 


6.748 


63 


8.176 


7.903 


7.403 


6.955 


6.553 


64 


7.879 


7.625 


7.156 


6.735 


6.355 


65 


7.584 


7.347 


6.908 


6.513 


6.156 


66 


7.291 


7.070 


6.660 


6.291 


5.955 


67 


7.000 


6.795 


6.413 


6.067 


5.753 


68 


6.712 


6.521 


6.167 


5.844 


5.551 


69 


6.428 


6.251 


5.922 


5.622 


5.348 


70 


6.146 


5.983 


5.678 


5.400 


5.145 


71 


5.869 


5.718 


5.437 


5.179 


4.942 


72 


5.596 


5.457 


5.198 


4.960 


4.740 


73 


5.327 


5.200 


4.962 


4.742 


4.540 


74 


5.063 


4.947 


4.729 


4.527 


4.340 


75 


4.805 


4.699 


4.499 


4.314 


4.142 


76 


4.551 


4.455 


4.273 


4.104 


3.946 


77 


4.303 


4.216 


4.050 


3.896 


3.752 


78 


4.061 


3.982 


3.832 


3.692 


3.561 


79 


3.825 


3.754 


3.618 


3.491 


3.372 


80 


3.595 


3.531 


3.409 


3.294 


3.187 


81 


3.370 


3.313 


3.204 


3.101 


3.004 


82 


3.150 


3.099 


3.002 


2.910 


2.823 


83 


2.934 


2.889 


2.803 


2.721 


2.643 


84 


2.720 


2.681 


2.605 


2.533 


2.464 


85 


2.508 


2.474 


2.408 


2.344 


2.284 


86 


2.298 


2.268 


2.210 


2.156 


2.103 


87 


2.088 


2.063 


2.013 


1.967 


1.922 


88 


1.879 


1.858 


1.817 


1.777 


1.739 


89 


1.673 


1.655 


1.621 


1.588 


1.556 


90 


1.471 


1.456 


1.428 


1.401 


1.375 


91 


1.272 


1.261 


1.238 


1.216 


1.195 


92 


1.081 


1.072 


1.054 


1.037 


1.020 


93 


0.899 


0.892 


0.879 


0.865 


0.852 


94 


0.731 


0.726 


0.716 


0.706 


0.696 


95 


0.580 


0.576 


0.569 


0.561 


0.554 


96 


0.459 


0.456 


0.450 


0.445 


0.439 


97 


0.365 


0.363 


0.359 


0.355 


0.351 


98 


0.239 


0.238 


0.236 


0.234 


0.232 


99 













TABJIiB XZZI. 

LIFE ANNUITIES— JOINT LIVES. 

Shewing the Values of Annuities on Two Joint Lives according to 
the combined experience of various Life Offices. 



Age. 1 


Per Cent. 


3 

Per Cent. 


3i 
Per Cent. 


4 
Per Cent. 


5 

Per Cent. 


6 
Per Cent. 


Older. 


Younger 


10 


10 


21.510 


19.726 


18.179 


16.832 


14.602 


12.851 


11 


11 


21.349 


19.595 


18.072 


16.744 


14.542 


12.808 


12 


12 


21.183 


19.460 


17.961 


16.652 


14.478 


12.763 


13 


13 


21.011 


19.320 


17.846 


16.556 


14.411 


12.715 


1% 


14 


20.834 


19.175 


17.726 


16.456 


14.341 


12.664 


15 


10 
15 


21.048 
20.652 


19.353 
19.026 


17.874 
17.602 


16.578 
16.353 


14.426 
14.268 


12.726 
12.611 


16 


11 
16 


20.873 
20.465 


19.210 

18.872 


17.756 
17.474 


16.480 
16.246 


14.357 
14.192 


12.676 
12.555 


17 


12 

17 


20.693 
20.274 


19.062 
18.713 


17.633 
17.342 


16.378 
16.135 


14.285 
14.112 


12.624 
12.497 


18 


13 

18 


20.508 
20.078 


18.909 
18.550 


17.506 
17.205 


16.272 
16.020 


14.210 
14.029 


12.569 
12.436 


19 


14 
19 


20.318 
19.877 


18.751 
18.382 


17.375 
17.064 


16.162 
15.901 


14.131 
13.943 


12.511 
12,372 


20 


10 
15 
20 


20.458 
20.123 
19.671 


18.866 
18.589 
18.209 


17.472 
17.239 
16.919 


16.243 
16.048 
15.778 


14.190 
14.049 
13.853 


12.556 
12.451 
12.305 


21 


11 
16 
21 


20.267 
19.923 
19.460 


18.708 
18.422 
18.032 


17.340 
17.099 
16.769 


16.133 
15.930 
15.651 


14.111 
13.964 
13.760 


12.498 
12.388 
12.236 


22 


12 
17 
22 


20.071 
19.718 
19.244 


18.545 
18.251 
17.850 


17.204 
16.955 
16.615 


16.018 
15.808 
15.520 


14.029 
13.875 
13.664 


12.437 
12.322 
12.164 


23 


13 
18 
23 


19.870 
19.508 
19.023 


18.377 
18.075 
17.663 


17.063 
16.806 
16.456 


15.899 
15.682 
15.384 


13.943 
13.783 
13.564 


12.373 
12.253 
12.089 


24 


14 
19 
24 


19.663 
19.293 
18.797 


18.204 
17.893 
17.471 


16.917 
16.653 
16.293 


15.776 
15.552 
15.244 


13.853 
13.687 
13.460 


12.307 
12.181 
12.010 


25 


10 
15 
20 
25 


19.722 
19.451 
19.073 
18.566 


18.255 
38.026 
17.707 
17.274 


16.960 
16.767 
16.495 
16.125 


15.811 
15.649 
15.417 
15.100 


13.881 
13.760 
13.587 
13.352 


12.329 
12.237 
12.106 
11.928 


26 


11 


19.512 


18.079 


16.811 


15.685 


13.789 


12.261 



TABXiB XZXZ. 

LIFE ANNUITIES— JOINT LIVES. 

Shewing the Values of Annuities on Two Joint Lives according to 
the combined experience of various Life Offices. 



Age. 


2^ 
Per Cent. 


3 
Per Cent. 


31 
Per Cent. 


4 
Per Cent. 


5 

Per Cent. 


6 

Per Cent. 


Older. 


Younger. 


26 


16 


19.234 


17.843 


16.612 


15.517 


13.663 


12.164 




21 


18.848 


17.516 


16.332 


15.278 


13.484 


12.028 




26 


18.329 


17.072 


15.952 


14.951 


13.240 


11.843 


27 


12 


19.296 


17.898 


16.658 


15.554 


13.693 


12.190 




17 


19.012 


17.655 


16.452 


15.381 


13..562 


12.088 




22 


18.617 


17.320 


16.165 


15.134 


13.377 


11.947 




27 


18.087 


16.865 


15.774 


14.797 


13.124 


11.754 


2a 


13 


19.075 


17.711 


16.499 


15.419 


13.593 


12.115 




18 


18.784 


17.462 


16.287 


15.240 


13.457 


12.009 




23 


18.381 


17.119 


15.993 


14.986 


13.266 


11.802 




28 


17.840 


16.652 


15.591 


14.638 


13.003 


11.661 


29 


14 


18.848 


17.519 


16.335 


15.279 


13.489 


12.037 




19 


18.551 


17.264 


16.118 


15.094 


13.348 


11.926 




24 


18.140 


16.913 


15.816 


14.833 


13.151 


11.774 




29 


17.587 


16.4.34 


15.403 


14.474 


12.878 


11.564 


30 


10 


18.827 


17.500 


16.321 


15.270 


13.484 


12.032 




15 


18.616 


17..321 


16.166 


1.5.134 


13.381 


11.955 




20 


18.313 


17.060 


15.943 


14.944 


13.235 


11.840 




25 


17.894 


16.701 


15.634 


14.675 


13.031 


11.682 




30 


17.329 


16.211 


15.209 


14.305 


12.749 


11.463 


31 


11 


18.594 


17.302 


16.152 


15.125 


13.376 


11.950 




16 


18.378 


17.118 


15.992 


14.984 


13.269 


11.869 




21 


18.069 


16.851 


15.763 


14.789 


13.118 


11.750 




26 


17.642 


16.484 


15.446 


14.512 


12.907 


11.586 




31 


17.065 


15.982 


15.010 


14.131 


12.615 


11.358 


32 


12 


18.355 


17.098 


15.977 


14.975 


13.263 


11.864 




17 


18.134 


16.909 


15.813 


14.829 


13.152 


11.779 




22 


17.820 


16.637 


15.578 


14.629 


12.996 


11.656 




27 


17.385 


16.262 


15.253 


14.344 


12.778 


11.486 




32 


16.796 


15.748 


14.805 


13.952 


12.476 


11.249 


33 


13 


18.110 


16.888 


15.797 


14.819 


13.145 


11.774 




18 


17.885 


16.695 


15.628 


14.669 


13.031 


11.685 




23 


17.565 


16.417 


15.388 


14.464 


12.870 


11. .558 




28 


17.122 


16.034 


15.055 


14.171 


12.645 


11.382 




33 


16.521 


15.508 


14.595 


13.767 


12.332 


11.135 


34L 


14 


17.859 


16.672 


15.611 


14.658 


13.023 


11.679 




19 


17.6.30 


16.475 


15.438 


14.504 


12.905 


11.587 




24 


17.305 


16.192 


15.192 


14.294 


12.739 


11.456 




29 


16.853 


15.800 


14.851 


13.992 


12.507 


11.273 




34 


16.240 


15.262 


14.379 


13.577 


12.183 


11.017 


35 


10 


17.765 


16.593 


15.544 


14.600 


12.978 


11.047 



TABLE XZZX. 

LIFE ANNUITIES— JOINT LIVES. 

Shewing the Values of Annuities on Two Joint Lives according to 
the combined experience of various Life Offices. 



Age. 


^ 


3 


31 


4 


5 


6 


Older. 


Younger. 


Per Cent. Per Cent, j 


Per Cent. J 


Per Cent. Per Cent.i'er ceni.i 


35 


15 


17.602 


16.450 


15.419 


14.491 


12.896 


11.580 




20 


17.369 


16.249 


15.242 


14.333 


12.774 


11.485 




25 


17.039 


15.961 


14.991 


14.118 


12.603 


11.349 




30 


16.578 


15.560 


14.641 


13.808 


12.363 


11.160 




35 


15.953 


15.010 


14.157 


13.381 


12.028 


10.893 


36 


11 


17.505 


16.368 


15.349 


14.431 


12.848 


11.546 




16 


17.339 


16.222 


15.221 


14.318 


12.763 


11.476 




21 


17.102 


16.017 


15.040 


14.157 


12.638 


11.378 




26 


16.767 


15.724 


14.784 


13.936 


12.462 


11.238 




31 


16.298 


15.315 


14.425 


13.618 


12.214 


11.042 




36 i 


15.660 


14.752 


13.928 


13.178 


11.867 


10.764 


37 


12 


17.238 


16.137 


15.148 


14.255 


12.713 


11.440 




17 


17.069 


15.988 


15.017 


14.139 


12.625 


11.368 




22 


16.829 


15.779 


14.832 


13.975 


12.497 


11.267 




27 


16.489 


15.481 


14.571 


13.749 


12.315 


11.122 




32 


16.011 


15.063 


14.203 


13.422 


12.060 


10.919 




37 


15.360 


14.487 


13.693 


12.969 


11.700 


10.629 


38 


13 


16.964 


15.899 


14.940 


14.073 


12.572 


11.329 




18 


16.792 


15.747 


14.806 


13.954 


12.481 


11.255 




23 


16.549 


15.535 


14.618 


13.787 


12.350 


11.150 




28 


16.204 


15.231 


14.351 


13.555 


12.163 


11.001 




33 


15.718 


14.805 


13.975 


13.220 


11.900 


10.791 




38 


15.053 


14.215 


13.451 


12.753 


11.526 


10.488 


39 


14 


1C.683 


15.654 


14.725 


13.884 


12.425 


11.212 




19 


16.509 


15.499 


14.589 


13.763 


12.331 


11.136 




24 


16.263 


15.284 


14.397 


13.592 


12.197 


11.028 




29 


15.913 


14.975 


14.125 


13.355 


12.005 


10.874 




34 


15.419 


14.540 


13.740 


13.011 


11.734 


10.657 




39 


14.740 


13.936 


13.202 


12.530 


11.346 


10.341 


^0 


10 


16.518 


15.609 


14.598 


13.772 


12.341 


11.147 




15 


16.395 


15.402 


14.503 


13.688 


12.271 


11.090 




20 


16.219 


15.244 


14.365 


13.565 


12.175 


11.011 




25 


15.970 


15.026 


14.170 


13.391 


12.038 


10.901 




30 


15.615 


14.712 


13.892 


13.148 


11.841 


10.742 




35 


15.113 


14.268 


13.498 


12.795 


11.561 


10.517 




40 


14.419 


13.049 


12.945 


12.299 


11.158 


10.187 


41 


11 


16.225 


15.251 


14.371 


13.571 


12.183 


11.021 




16 


16.100 


15.142 


14.274 


13.485 


12.111 


10.962 




21 


15.922 


14.982 


14.134 


13.360 


12.012 


10.880 




26 


15.670 


14.761 


13.936 


13.183 


11.872 


10.767 




31 


15.310 


14.442 


13.652 


12.934 


11.670 


10.604 




36 


14.800 


13.989 


13.249 


12.572 


11.381 


10.370 




41 


14.091 


13.354 


12.680 


12.060 


10.963 


10.025 


42 


12 


15.924 


14.986 


14.136 


13.363 


12.018 


10.888 



TABZiB XIZZ. 

LIFE ANNUITIES— JOINT LIVES. 

Shewing the Values of Annuities on Two Joint Lives according to 
the combined experience of various Life Offices. 



A 


ge. 


01 

Per Cent 


3 

Per Cent 


3^ 
Per Cent 


4 
Per Cent 


5 
. Per Cent 


6 
, Per Cent. 


Older. 


Younger 


42 


17 


15.797 


14.875 


14.037 


13.275 


11.944 


10.827 




22 


15.618 


14.713 


13.895 


13.148 


11.843 


10.743 




27 


15.363 


14.480 


13.694 


12.968 


11.699 


10.627 




32 


14.998 


14.165 


13.405 


12.713 


11.492 


10.459 




37 


14.480 


13.703 


12.993 


12.342 


11.194 


10.216 




42 


13.755 


13.051 


12.407 


11.813 


10.759 


9.856 


4:3 


13 


15.615 


14.713 


13.893 


13.147 


11.845 


10.748 




18 


15.487 


14.600 


13.793 


13.057 


11.770 


10.686 




23 


15.306 


14.437 


13.649 


12.928 


11.667 


10.600 




28 


15.049 


14.210 


13.445 


12.745 


11.519 


10.481 




33 


14.679 


13.881 


13.151 


12.485 


11.307 


10.308 




38 


14.152 


13.409 


12.729 


12.104 


10.999 


10.055 




43 


13.411 


12.740 


12.126 


11.558 


10.547 


9.679 


44: 


14 


15.299 


14.4.33 


13.643 


12.924 


11.665 


10.602 




19 


15.170 


14.318 


13.542 


12.832 


11.589 


10.538 




24 


14.988 


14.154 


13.396 


12.702 


11.484 


10.451 




29 


14.729 


13.924 


13.189 


12.516 


11.333 


10.328 




34 


14.354 


13.590 


12.890 


12.250 


11.116 


10.150 




39 


1.3.818 


13.108 


12.458 


11.869 


10.797 


9.887 




44 


13.061 


12.423 


11.838 


11.295 


10.328 


9.495 


45 


10 


15.067 


14.226 


13.462 


12.761 


11.533 


10.494 




15 


14.977 


14.146 


13.387 


12.695 


11.479 


10.450 




20 


14.848 


14.030 


13.285 


12.601 


11.402 


10.385 




25 


14.665 


13.865 


13.137 


12.470 


11.295 


10.296 




30 


14.403 


13.633 


12.927 


12.281 


11.141 


10.170 




35 


14.024 


13.293 


12.G23 


12.009 


10.918 


9.986 




40 


13.478 


12.801 


12.180 


11.607 


10.588 


9.713 




45 


12.706 


12.100 


11.544 


11.027 


10.103 


9.304 


46 


11 


14.741 


13.935 


13.201 


12.527 


11.343 


10.338 




16 


14.650 


13.854 


13.125 


12.460 


11.287 


10.292 




21 


14.520 


13.737 


13.022 


12.364 


11.209 


10.226 




26 


14.337 


13.571 


12.873 


12.232 


11.100 


10.135 




31 


14.073 


13..336 


12.660 


12.040 


10.943 


10.006 




36 


13.689 


12.991 


12.350 


11.762 


10.714 


9.816 




41 


13.132 


12.488 


11.896 


11.349 


10.373 


9.532 




46 


12.348 


11.773 


11.245 


10.753 


9.872 


9.108 


47 


12 


14.411 


13.639 


12.935 


12.288 


11.147 


10.177 




17 


14.319 


13.557 


12.858 


12.219 


11.090 


10.129 




22 


14.189 


13.440 


12.754 


12.123 


11.011 


10.062 




27 


14.005 


13.273 


12.604 


11.989 


10.900 


9.969 




32 


13.739 


13.035 


12.388 


n.794 


10.740 


9.837 




37 


13.350 


12.085 


12.073 


11.510 


10.505 


9.641 




42 


12.782 


12.170 


11.606 


11.085 


10.152 


9.345 




47 


11.988 


11.444 


10.943 


10.470 


9.637 


8.907 


48 


13 


14.076 


13.338 


12.664 


12.043 


10.946 


10.010 



TABXiS XXXX. 

LIFE ANNUITIES— JOINT LIVES. 

Shewing the Values of Annuities on Two Joint Lives according to 
the combined experience of various Life Offices. 



Age. 


2| 
Per Cent 


3 
Per Cent. 


31 
Per Cent. 


4 
Per Cent. 


5 6 

Per Cent. Per Cent. 

1 


Older. 1 Younger. 




48 


18 


13.984 


13.256 


12.586 


11.974 


10.888 


9.961 




23 


13.854 


13.138 


12.482 


11.877 


10.808 


9.893 




28 


13.669 


12.970 


12.331 


11.741 


10.695 


9.798 




33 


13.401 


12.730 


12.112 


11.544 


10.532 


9.664 




38 


13.007 


12.374 


11.791 


11.253 


10.291 


9.461 




43 


12.4-27 


11.847 


11.311 


10.815 


9.925 


9.152 




48 


11.627 


11.113 


10.638 


10.196 


9.399 


8.702 


49 


14 


13.738 


13.033 


12.389 


11.794 


10.740 


9.838 




19 


13.645 


12.951 


12.310 


11.724 


10.681 


9.788 




24 


13.516 


12.833 


12.206 


11.626 


10.600 


9.720 




29 


13.330 


12.664 


12.053 


11.489 


10.486 


9.623 




34 


13.060 


12.421 


11.832 


11.289 


10.319 


9.485 




39 


12.660 


12.059 


11.504 


10.991 


10.072 


9.275 




44 


12.069 


11.520 


11.011 


10.540 


9.692 


8.953 




49 


11.265 


10.780 


10..331 


9.913 


9.156 


8.493 


50 


10 


13.461 


12.783 


12.161 


11.588 


10.570 


9.696 




15 


13.396 


12.724 


12.109 


11.540 


10.529 


9.661 




20 


13.303 


12.642 


12.030 


11.469 


10.469 


9.610 




25 


13.174 


12.524 


11.925 


11.371 


10.388 


9.541 




30 


12.988 


12.354 


11.771 


11.233 


10.272 


9.443 




35 


12.716 


12.108 


11.548 


11.030 


10.102 


9.301 




40 


12.310 


11.740 


11.212 


10.724 


9.847 


9.084 




45 


11.709 


11.190 


10.708 


10.261 


9.454 


8.749 




50 


10.902 


10.446 


10.022 


9.627 


8.910 


8.280 


51 


11 


13.116 


12.471 


11.878 


11.330 


10.355 


9.515 




16 


13.051 


12.411 


11.825 


11.281 


10.313 


9.479 




21 


12.958 


12.329 


11.746 


11.210 


10.253 


9.428 




26 


12.829 


12.211 


11.640 


11.112 


10.171 


9.358 




31 


12.643 


12.041 


11.486 


10.973 


10.053 


9.258 




36 


12.369 


11.792 


11.260 


10.766 


9.880 


9.113 




41 


11.956 


11.417 


10.916 


10.452 


9.617 


8.888 




46 


11.347 


10.857 


10.401 


9.978 


9.212 


8.541 




51 


10.539 


10.111 


9.712 


9.339 


8.661 


8.063 


52 


12 


12.768 


12.155 


11.591 


11.068 


10.135 


9.329 




17 


12.703 


12.095 


11.537 


11.018 


10.092 


9.292 




22 


12.611 


12.013 


11.458 


10.947 


10.032 


9.241 




27 


12.482 


11.895 


11.352 


10.849 


9.950 


9.170 




32 


12.296 


11.725 


11.197 


10.708 


9.830 


9.069 




37 


12.020 


11.473 


10.968 


10.498 


9.653 


8.920 




42 


11.599 


11.090 


10.616 


10.175 


9.381 


8.686 




47 


10.984 


10.523 


10.093 


9.693 


8.966 


8.329 




52 


10.177 


9.776 


9.401 


9.049 


8.409 


7.843 


53 


13 


12.418 


11.836 


11.300 


10.801 


9.911 


9.138 




18 


12.353 


11.776 


11.245 


10.751 


9.867 


9.101 




23 


12.262 


11.694 


11.167 


10.680 


9.807 


9.049 




28 


12.133 


11.576 


11.061 


10.582 


9.724 


8.978 



TABZiS XZZX. 

LIFE ANNUITIES— JOINT LIVES. 

Shewing the Values of Annuities on Two Joint Lives accordino- to 
the combined experience of various Life Offices. 



Age. 


2^ 
Per Cent. 


3 

Per Cent. 


3i 
Per Cent. 


4 
Per Cent. 


5 
Per Cent. 


Per Cent. 


Older. 


Younger' 


53 


33 


11.947 


11.406 


10.905 


10.440 


9.603 


8.876 




38 


11.668 


11.151 


10.672 


10.226 


9.422 


8.722 




43 


11.240 


10.760 


10.312 


9.894 


9.140 


8.479 




48 


10.021 


10.188 


9.783 


9.405 


8.718 


8.113 




53 


9.816 


9.441 


9.089 


8.758 


8.150 


7.621 


54 


14 


12.066 


11.514 


11.005 


10.531 


9.682 


8.943 




19 


12.001 


11.454 


10.950 


10.481 


9,638 


8.905 




24 


11.911 


11.373 


10.873 


10.410 


9.578 


8.854 




29 


11.782 


11.255 


10.767 


10.312 


9.494 


8.782 




34 


11.596 


11.085 


10.610 


10.169 


9.372 


8.678 




39 


11.314 


10.826 


10.373 


9.950 


9.187 


8.519 




44 


10.879 


10.427 


10.004 


9.609 


8.895 


8.266 




49 


10.259 


9.853 


9.472 


9.116 


8.467 


7.894 




54 


9.457 


9.106 


8.776 


8.466 


7.900 


7.395 


55 


10 


11.755 


11.232 


10.746 


10.294 


9.479 


8.770 




15 


11.712 


11.189 


10.707 


10.257 


9.449 


8.743 




20 


11.647 


11.130 


10.652 


10.207 


9.405 


8.705 




25 


11.558 


11.049 


10.576 


10.136 


9.345 


8.053 




30 


11.4.30 


10.932 


10.470 


10.038 


9.260 


8.581 




35 


11.244 


10.761 


10.312 


9.894 


9.137 


8.475 




40 


10.958 


10.499 


10.071 


9.671 


8.947 


8.312 




45 


10.517 


10.092 


9.694 


9.321 


8.646 


8.050 




50 


9.898 


9.517 


9.160 


8.825 


8.214 


7. 072 




55 


9.099 


8.772 


8.464 


8.174 


7.642 


7.167 


56 


11 


11.400 


10.906 


10.446 


10.017 


9.243 


8.567 




16 


11.356 


10.862 


10.406 


9.980 


9.212 


8.539 




21 


11.292 


10.804 


10.352 


9.930 


9.168 


8.501 




26 


11.204 


10.724 


10.276 


9.859 


9.108 


8.449 




31 


11.077 


10.607 


10.170 


9.761 


9.023 


8.376 




36 


10.891 


10.436 


10.012 


9.616 


8.899 


8.269 




41 


10.601 


10.169 


9.766 


9.388 


8.703 


8.100 




46 


10.155 


9.756 


9.382 


9.031 


8.394 


7.830 




51 


9.538 


9.182 


8.847 


8.533 


7.958 


7.447 




56 


8.745 


8.440 


8.153 


7.882 


7.384 


6.938 


57 


12 


11.043 


10.578 


10.143 


9.737 


9.003 


8.359 




17 


11.000 


10.534 


10.103 


9.700 


8.971 


8.331 




22 


10.936 


10.476 


10.049 


9.650 


8.928 


8.293 




27 


10.849 


10.397 


9.974 


9.580 


8.808 


8.241 




32 


10.723 


10.281 


9.868 


9.482 


8.783 


8.168 




37 


10.537 


10.109 


9.709 


9.336 


8.056 


8.058 




42 


10.243 


9.837 


9.458 


9.102 


8.455 


7.884 




47 


9.794 


9.420 


9.069 


8.740 


8.140 


7.607 




52 


9.181 


8.848 


8.535 


8.241 


7.701 


7.219 




57 


8.393 


8.110 


7.842 


7.590 


7.124 


6.706 


5S 


13 


10.685 


10.248 


9.837 


9.454 


8.759 


8.147 




18 


10.642 


10.204 


9.797 


9.417 


8.727 


8.119 



TABXiS XZXX. 

LIFE ANNUITIES— JOINT LIVES. 

Shewing the Values of Annuities on Two Joint Lives according to 
the combined experience of various Life Offices. 



Age. 


^ 


3 


31 


4 


5 


6 


Older. 


Younger. 


Per Cent. 


Per Cent. 


Per Cent. 


Per Cent.rer Uent. 


Per Cent. 


58 


23 


10.580 


10.147 


9.744 


9.367 


8.683 


8.081 




28 


10.494 


10.068 


9.670 


9.299 


8.624 


8.029 




33 


10.369 


9.953 


9.565 


9.200 


8.539 


7.955 




38 


10.182 


9.780 


9.404 


9.052 


8.410 


7.843 




43 


9.883 


9.503 


9.147 


8.813 


8.203 


7.662 




48 


9.434 


9.084 


8.756 


8.447 


7.883 


7.380 




53 


8.824 


8.515 


8.223 


7.948 


7.442 


6.990 




58 


8.043 


7.781 


7.533 


7.298 


6.864 


6.473 


59 


14 


10.327 


9.916 


9.529 


9.168 


8.511 


7.931 




19 


10.284 


9.873 


9.490 


9.131 


8.479 


7.903 




24 


10.223 


9.817 


9.437 


9.082 


8.436 


7.865 




29 


10.138 


9.739 


9.364 


9.014 


8.377 


7.813 




34 


10.015 


9.625 


9.259 


8.916 


8.292 


7.739 




39 


9.827 


9.450 


9.097 


8.766 


8.161 


7.625 




44 


9.523 


9.168 


8.834 


8.521 


7.947 


7.437 




49 


9.075 


8.749 


8.442 


8.154 


7.624 


7.151 




54 


8.471 


8.183 


7.911 


7.655 


7.182 


6.758 




59 


7.697 


7.455 


7.225 


7.007 


6.603 


6.238 


60 


10 


10.109 


9.611 


9.246 


8.905 


8.282 


7.730 




15 


9.969 


9.583 


9.220 


8.880 


8.260 


7.711 




20 


9.926 


9.541 


9.181 


8.844 


8.229 


7.683 




25 


9.866 


9.486 


9.129 


8.795 


8.186 


7.646 




30 


9.783 


9.409 


9.057 


8.728 


8.127 


7.594 




35 


9.661 


9.295 


8.952 


8.630 


8.041 


7.519 




40 


9.472 


9.119 


8.788 


8.477 


7.908 


7.402 




45 


9.164 


8.833 


8.521 


8.227 


7.689 


7.209 




50 


8.719 


8.415 


8.129 


7.860 


7.364 


6.920 




55 


8.120 


7.853 


7.601 


7.362 


6.921 


6.524 




60 


7.355 


7.131 


6.919 


6.717 


6.342 


6.003 


61 


11 


9.643 


9.278 


8.936 


8.615 


8.029 


7.508 




16 


9.612 


9.250 


8.910 


8.590 


8.007 


7.489 




21 


9.569 


9.209 


8.872 


8.555 


7.976 


7.461 




26 


9.511 


9.155 


8.821 


8.507 


7.933 


7.423 




31 


9.429 


9.079 


8.750 


8.440 


7.875 


7.372 




36 


9.308 


8.966 


8.645 


8.343 


7.789 


7.296 




41 


9.117 


8.788 


8.479 


8.187 


7.653 


7.177 




46 


8.807 


8.498 


8.207 


7.933 


7.429 


6.978 




51 


8.365 


8.084 


7.818 


7.566 


7.103 


6.687 




56 


7.774 


7.527 


7.293 


7.071 


6.661 


6.290 




61 


7.018 


6.812 


6.616 


6.429 


6.083 


5.767 


62 


12 


9.287 


8.946 


8.626 


8.325 


7.774 


7.283 




17 


9.256 


8.918 


8.600 


8.300 


7.752 


7.263 




22 


9.214 


8.878 


8.563 


8^/65 


7.721 


7.236 




27 


9.157 


8.825 


8.512 


8.218 


7.679 


7.199 




32 


9.077 


8.750 


8.442 


8.152 


7.621 


7.147 




37 


8.957 


8.638 


8.338 


8.055 


7.535 


7.072 




42 


8.763 


8.457 


8.168 


7.896 


7.396 


0.948 



TABX.E XXIX. 

LIFE ANNUITIES— JOINT LIVES. 

Shewing tlie Values of Annuities on Two Joint Lives according to 
the combined experience of various Life Offices. 





Age. 


^ 


1 
3 


3^ 


4 


5 


_ 1 






Per Cent.lPer Cent.' J 


Per Cent. Per (Jent.lJ 


Per Cent. Per <Jont.| 




Older. '' 

62 


I oungerJ 
















47 


8.453 


8.166 


7.895 


7.639 


7.168 


0.745 






52 


8.016 


7.755 


7.508 


7.274 


6.843 


6.453 






57 


7.432 


7.204 


6.987 


6.782 


6.401 


6.055 






62 


6.687 


6.497 


6.317 


6.145 


5.825 


5.532 




63 


13 


8.933 


8.616 


8.317 


8.035 


7.518 


7.056 






18 


8.903 


8.588 


8.290 


8.010 


7.496 


7.036 






23 


8.862 


8.549 


8.254 


7.976 


7.465 


7.009 






28 


8.806 


8.496 


8.205 


7.930 


7.424 


6.972 






33 


8.727 


8.423 


8.136 


7.865 


7.367 


6.921 






38 


8.608 


8.311 


8.031 


7.767 


7.280 


6.845 






43 


8.412 


8.127 


7.859 


7.605 


7.137 


6.717 






48 


8.103 


7.837 


7.585 


7.347 


6.907 


6.511 






53 


7.671 


7.430 


7.201 


6.984 


6.582 


6.219 






58 


7.095 


6.884 


6.685 


6.495 


6.142 


5.821 






63 


6.362 


6.188 


6.022 


5.864 


5.569 


5.299 




64 


14 


8.582 


8.287 


8.008 


7.745 


7.261 


6.827 






19 


8.553 


8.259 


7.982 


7.720 


7.239 


6.807 






24 


8.513 


8.221 


7.946 


7.687 


7.209 


6.781 






29 


8.458 


8.170 


7.898 


7.641 


7.168 


6.744 






34 


8.381 


8.098 


7.830 


7.577 


7.112 


6.693 






39 


8.262 


7.986 


7.725 


7.479 


7.025 


6.616 






44 


8.063 


7.799 


7.550 


7.313 


6.877 


6.484 






49 


7.757 


7.510 


7.277 


7.056 


6.647 


6.277 






54 


7.331 


7.108 


6.897 


6.696 


6.323 


5.985 






59 


6.763 


6.570 


6.385 


6.210 


5.884 


5.586 






C4 


6.044 


5.885 


5.733 


5.588 


5.316 


5.067 




65 


10 


8.255 


7.979 


7.719 


7.473 


7.019 


6.611 






15 


8.235 


7.961 


7.701 


7.456 


7.004 


6.597 






20 


8.206 


7.933 


7.675 


7.432 


6.982 


6.578 






25 


8.167 


7.897 


7.641 


7.399 


6.953 


6.551 






30 


8.114 


7.847 


7.594 


7.354 


6.913 


6.515 






35 


8.039 


7.775 


7.527 


7.291 


6.857 


6.465 






40 


7.919 


7.664 


7.421 


7.192 


6.768 


6.386 






45 


7.718 


7.474 


7.243 


7.024 


6.618 


6.251 






50 


7.416 


7.188 


6.973 


6.768 


6.388 


6.043 






55 


6.997 


6.791 


6.596 


6.410 


6.065 


5.751 






CO 


6.437 


6.260 


6.091 


5.929 


5.628 


5.353 






65 


5.734 


5.588 


5.450 


5.317 


5.068 


4.838 




66 


11 


7.912 


7.656 


7.414 


7.185 


6.762 


6.380 






16 


7.892 


7.637 


7.397 


7.168 


6.747 


6.367 






21 


7.804 


7.611 


7.371 


7.145 


6.726 


6.347 






26 


7.826 


7.575 


7.338 


7.113 


6.697 


6.321 






31 


7.775 


7.527 


7.292 


7.069 


6.658 


6.286 






36 


7.700 


7.457 


7.226 


7.007 


6.602 


6.236 






41 


7.581 


7.344 


7.120 


6.907 


6.512 


6.15(5 






46 


7.379 


7.153 


6.939 


6.736 


6.359 


6.017 






51 


7.081 


6.871 


6.672 


6.482 


6.130 


5.810 



TABXaXS XZZX. 

LIFE ANNUITIES— JOINT LIVES. 

Shewing the Values of Annuities on Two Joint Lives according to 
the combined experience of various Life Offices. 



Age. 


n 


3 


3| 


4 


5 


6 






Per Cent. 


Per Cent. 


Per Cent. 


Per Cent. 


Per Cent. 


Per Cent. 


Older. 


Younger. 














66 


56 


6.668 


6.480 


6.300 


6.129 


5.810 


5.518 




61 


6.118 


5.956 


5.801 


6.653 


5.376 


5.122 




66 


5.431 


5.299 


5.173 


5.051 


4.823 


4.612 


67 


12 


7.573 


7.336 


7.112 


6.900 


6.506 


6.150 




17 


7.553 


7.318 


7.095 


6.883 


6.491 


6.136 




22 


7.526 


7.292 


7.070 


6.8G0 


6.470 


6.117 




27 


7.490 


7.258 


7.038 


6.829 


6.442 


6.092 




32 


7.440 


7.210 


6.993 


6.786 


6.404 


6.057 




37 


7.367 


7.141 


6.928 


6.725 


6.348 


6.007 




42 


7.246 


7.028 


6.820 


6.623 


6.257 


5.925 




47 


7.044 


6.837 


6.639 


6.451 


6.102 


5.784 




52 


6.752 


6.559 


6.375 


6.200 


5.874 


5.577 




57 


6.347 


6.174 


6.009 


5.851 


5.557 


5.287 




62 


5.807 


5.658 


5.516 


5.381 


5.126 


4.892 




67 


5.138 


5.018 


4.902 


4.792 


4.583 


4.390 


68 


13 


7.240 


7.021 


6.814 


6.617 


6.251 


5.920 




18 


7.220 


7.003 


6.797 


6.601 


6.236 


5.906 




23 


7.194 


6.978 


6.773 


6..578 


6.216 


5.887 




28 


7.159 


6.945 


6.741 


6.548 


6.189 


5.862 




33 


7.111 


6.899 


0.698 


6.507 


6.151 


5.828 




38 


7.038 


6.831 


6.633 


6.445 


6.096 


5.779 




43 


6.917 


6.715 


6.524 


6.342 


6.003 


5.694 




48 


6.717 


6.525 


6.343 


6.170 


5.847 


5.552 




53 


6.429 


6.252 


6.083 


5.922 


5.622 


5.347 




58 


6.032 


5.874 


5.722 


5.578 


5.307 


5.058 




63 


5.503 


5.368 


5.238 


5.114 


4.881 


4.666 




68 


4.853 


4.744 


4.639 


4.539 


4.349 


4.172 


69 


14 


6.912 


6.711 


6.520 


6.337 


5.999 


5.690 




19 


6.893 


6.693 


6.503 


6.321 


5.984 


5.677 




24 


6.868 


6.669 


6.480 


6.300 


5.964 


5.659 




29 


6.834 


6.637 


6.449 


6.270 


5.937 


5.634 




34 


6.787 


6.592 


6.407 


6.230 


5.901 


5.601 




39 


6.716 


6.525 


6.343 


6.169 


5.846 


5.551 




44 


6.592 


6.408 


6.231 


6.063 


5.750 


5.464 




49 


6.396 


6.220 


6.053 


5.893 


5.595 


5.322 




54 


6.114 


5.952 


5.797 


5.649 


5.372 


5.118 




59 


5.724 


5.580 


5.441 


5.309 


5.060 


4.832 




64 


5.208 


5.085 


4.967 


4.854 


4.641 


4.444 




69 


4.578 


4.479 


4.384 


4.293 


4.120 


3.959 


70 


10 


6.602 


6.417 


6.240 


6.071 


5.757 


5.471 




15 


6.590 


6.405 


6.229 


6.061 


5.748 


5.462 




20 


6.572 


6.388 


6.212 


6.045 


5.733 


5.449 




25 


6.548 


6.364 


6.190 


6.024 


5.714 


5.431 




30 


6.515 


6.333 


6.160 


5.996 


5.688 


5.407 




35 


6.469 


6.290 


6.119 


5.957 


5.652 


5.374 




40 


6.399 


6.223 


6.056 


5.896 


5.597 


5.325 




45 


6.274 


6.105 


5.943 


5.788 


5.500 


5.235 



TABZiS XZIZ. 

LIFE ANNUITIES— JOINT LIVES. 

Shewing the Values of Annuities on Two Joint Lives according to 
the combined experience of various Life Offices. 



Age. 


2^ 


3 


3^ 


4 


5 
Per Cent. 


6 
Per Cent. 


Older, 


younger. 


Per Cent 


Per Cent. 


Per Cent, rer i^eni. 


70 


50 


6.081 


5.920 


5.767 


5.620 


5.346 


5.094 




55 


5.806 


5.657 


5.516 


5.380 


5.126 


4.892 




60 


5.424 


5.292 


5.166 


5.045 


4.817 


4.607 




65 


4.921 


4.809 


4.702 


4.599 


4.405 


4.225 




70 


4.311 


4.222 


4.136 


4,054 


3.897 


3.751 


71 


11 


6.286 


6.116 


5.954 


5.799 


5.509 


5.244 




16 


6.274 


6.105 


5.943 


5.788 


5.499 


5.235 




21 


6.257 


6.088 


5.927 


5.773 


5.485 


5.222 




26 


6.233 


6.066 


5.905 


5.753 


5.466 


5.205 




31 


6.202 


6.036 


5.877 


5.725 


5.441 


5.181 




36 


6.158 


5.994 


5.837 


5.687 


5.407 


5.150 




41 


6.088 


5.927 


5.773 


5.626 


5.351 


5.099 




46 


5.963 


5.808 


5.659 


5.518 


5.252 


5.008 




51 


5.774 


5.627 


5.487 


5.352 


5.100 


4.868 




56 


5.505 


5.370 


5.240 


5.116 


4.883 


4.668 




61 


5.132 


6.012 


4.897 


4.787 


4.579 


4.386 




66 


4.643 


4.542 


4.445 


4.351 


4.175 


4.010 




71 


4.054 


3.974 


3.896 


3.822 


3,680 


. 3.547 


72 


12 


5.977 


5.821 


5.672 


5.530 


5.263 


5.018 




17 


5.965 


5.810 


5.662 


5.520 


5.254 


5.010 




22 


5.948 


5.794 


5.646 


5.505 


5.240 


4.997 




27 


5.926 


5.772 


5.626 


5.485 


5.222 


4.980 




32 


5.696 


5.744 


5.598 


5.459 


5.198 


4.958 




37 


5.853 


5.703 


5.559 


5.422 


5.164 


4.927 




42 


5.783 


5.636 


5.495 


5.360 


5.108 


4.875 




47 


5.659 


5.517 


5.381 


5.251 


5.008 


4.783 




52 


5.474 


5.340 


5.212 


5.089 


4.858 


4.645 




57 


5.212 


5.089 


4.971 


4.858 


4.645 


4.447 




62 


4.847 


4.739 


4.634 


4.534 


4.345 


4.169 




67 


4.374 


4.283 


4.195 


4.110 


3.950 


3.800 




72 


3.806 


3,734 


3.664 


3.597 


3.469 


3.348 


73 


13 


5.675 


6.532 


5.396 


5.266 


5.021 


4.795 




18 


5.663 


5.521 


5.385 


5.255 


5.011 


4.787 




23 


5.647 


5.506 


5.371 


5.241 


4.998 


4.774 




28 


5.625 


5.485 


5.351 


5.222 


4.981 


4.758 




33 


5.597 


5.458 


5.324 


5.197 


4.957 


4.737 




38 


5.555 


5.418 


5.287 


5.161 


4.924 


4.706 




43 


5.484 


5.350 


5.221 


5.098 


4.867 


4.653 




48 


5.362 


5.233 


5.109 


4.990 


4.767 


4.561 




53 


5.182 


5.061 


4.944 


4.832 


4.621 


4.425 




58 


4.927 


4.815 


4.708 


4.605 


4.411 


4.230 




63 


4.572 


4.474 


4.379 


4.288 


4.116 


3.955 




68 


4.114 


4.032 


3.953 


3.876 


3.731 


3.595 




73 


3.568 


3.503 


3.440 


3.380 


3.264 


3.155 


74 


14 


5.379 


5.249 


5.125 


5.006 


4.782 


4.575 




19 


5.368 


5.238 


5.115 


4.996 


4.772 


4.566 




24 


5.352 


5.224 


5.100 


4.982 


4.760 


4.554 




29 


6.332 


5.-204 


5.082 


4.964 


4.743 


4.539 



a 



LIFE ANNUITIES— JOINT LIVES. 

Shewino: the Values of Annuities on Two Joint Lives according to 
the combined experience of various Life Offices. 



Age. 


2| 
Per Cent. 


3 
Per Cent. 


31 
Per Cent. 


4 
Per Cent. 


5 

Per Cent. 


6 


Older. 


Younger. 


Per Cent. 


74 


34 


5.304 


5.178 


5.056 


4.940 


4.720 


4.518 




39 


5.264 


5.139 


5.019 


4.904 ' 


4.688 


4.488 




44 


5.192 


5.070 


4.953 


4.841 


4.629 


4.43? 




49 


5.073 


4.955 


4.843 


4.735 


4.531 


4.342 




54 


4.898 


4.788 


4.682 


4.580 


4.387 


4.208 




59 


4.649 


4.548 


4.451 


4.358 


4.181 


4.016 




64 


4.305 


4.216 


4.131 


4.048 


3.892 


3.746 




69 


3.864 


3.790 


3.718 


3.649 


3.518 


3.395 




74 


3.338 


3.280 


3.224 


3.170 


3.066 


2.968 


75 


10 


5.097 


4.979 


4.866 


4.757 


4.552 


4.362 




15 


5.090 


4.973 


4.860 


4.751 


4.546 


4.357 




20 


5.080 


4.962 


4.850 


4.741 


4.537 


4.348 




25 


5.065 


4.948 


4.836 


4.728 


4.525 


4.337 




30 


5.045 


4.929 


4.818 


4.711 


4.509 


4.322 




35 


5.019 


4.904 


4.794 


4.688 


4.487 


4.302 




40 


4.!)80 


4.8G6 


4.757 


4.653 


4.455 


4.272 




45 


4.907 


4.797 


4.691 


4.588 


4.395 


4.217 




50 


4.791 


4.685 


4.583 


4.485 


4.299 


4.127 




55 


4.622 


4.522 


4.426 


4.333 


4.158 


3.995 




60 


4.380 


4.289 


4.201 


4.116 


3.956 


3.806 




65 


4.047 


3.967 


3.890 


3.815 


3.674 


3.542 




70 


3.623 


3.556 


3.492 


3.430 


3.311 


3.200 
2.786 




75 


3.118 


3.006 


3.016 


2.967 


2.874 


7S 


11 


4.816 


4.709 


4.607 


4.508 


4.321 


4.147 




16 


4.809 


4.703 


4.600 


4.501 


4.315 


4.142 




21 


4.799 


4.693 


4.590 


4.492 


4.306 


4.134 




26 


4.785 


4.679 


4.577 


4.480 


4.295 


4.123 




31 


4.767 


4.661 


4.560 


4.463 


4.279 


4.108 




36 


4.742 


4.638 


4.537 


4.441 


4.258 


4.089 




41 


4.703 


4.600 


4.501 


4.406 


4.226 


4.059 




46 


4.630 


4.530 


4.434 


4.341 


4166 


4.003 




51 


4.518 


4.422 


4.329 


4.240 


4.072 


3.915 




56 


4.354 


4.264 


4.177 


4.093 


3.934 


3.786 




61 


4.119 


4.037 


3.958 


3.881 


3.736 


3.600 




66 


3.798 


3.726 


3.657 


3.589 


3.462 


3.342 




71 


3.390 


3.331 


3.274 


3.218 


3.111 


3.011 




76 


2.907 


2.861 


2.816 


2.773 


2.689 


2.610 


77 


12 


4.542 


4.446 


4.353 


4.263 


4.093 


3.935 




17 


4.535 


4.439 


4.346 


4.257 


4.087 


3.930 




22 


4.526 


4.429 


4.337 


4.248 


4.079 


3.922 




27 


4.512 


4.417 


4.325 


4.236 


4.068 


3.911 




32 


4.495 


4.400 


4.308 


4.220 


4.053 


3.898 




37 


4.471 


4.377 


4.287 


4.199 


4.034 


3.879 




42 


4.433 


4.340 


4.251 


4.164 


4.001 


3.849 




47 


4.361 


4.271 


4.184 


4.100 


3.941 


3.793 




52 


4.252 


4.166 


4.082 


4.002 


3.849 


3.707 




57 


4.094 


4.013 


3.935 


3.859 


3.716 


3.581 




62 


3.867 


3.793 


3.722 


3.653 


3.522 


3.399 




67 


3.557 


3.493 


3.431 


3.371 


3.256 


3.148 



TABZiE XZZZ. 

LIFE ANNUITIES-JOINT LIVES. 

Shewing the Values of Annuities on Two Joint Lives according to 
the couibined experience of various Life Offices. ° 

I 



Age. 


21 


3 3^- 4 

t.Per Cent. Per Cent.lPer Cent 

1 1 


5 
,. Per Cent 


6 
t. Per Cent. 


Older 


Yo . gerF^' Cen 


77 


72 


' 3.167 


3.114 


j 3.063 


3.013 


2.918 


2.828 




77 


2.704 


2.664 


1 2.624 

1 


2.585 


2.511 


2.440 


7a 


13 


4.276 


4.189 


1 4.105 


4.024 


3.870 


3.727 




18 


4.269 


4.182 


1 4.099 


4.018 


3.865 


3.721 




23 


4.260 


4.173 


4.090 


4.010 


3.857 


3.714 




28 


4.247 


4.161 


4.078 


3.998 


3.846 


3.704 




33 


4.231 


4.146 


4.063 


3.983 


3.832 


3.691 




38 


4.209 


4.124 


i 4.042 


3.963 


3.813 


3.673 




43 


4.170 


4.086 


i 4.006 


3.928 


3.780 


3.642 




48 


4.100 


4.019 


j 3.940 


3.865 


3.721 


; 3.587 




53 


3.995 


3.917 


1 3.842 


3.770 


3.632 


1 3.503 




58 


3.843 


3.770 


, 3.699 


3.631 


3.502 


3.380 




63 


3.623 


3.557 


; 3.493 


3.431 


3.313 


3.202 




68 


3.326 


3.269 


3.213 


3.1.59 


3.056 


2.959 




73 


2.954 


2.906 


i 2.861 


2.816 


2.731 


i 2.650 




78 


2.511 


2.475 


i 2.440 


2.405 


2.339 


I 2.276 


79 


14 


4.017 


3.939 


i 3.864 


3.791 


3.652 


3.522 




19 


4.011 


3.933 


i 3.858 


3.785 


3.647 


3.517 




24 


4.002 


3.924 


1 3.849 


3.777 


3.639 


3.510 




29 


3.990 


3.913 


' 3.838 


3.766 


3.629 


3.500 




34 


3.975 


3.898 


3.824 


3.752 


3.616 


3.488 




39 


3.954 


3.878 


3.804 


3.733 


3.598 


3 471 




44 


3.914 


3.840 


3.767 


3.697 


3.564 


3.440 




49 


3.847 


3.774 


3.704 


3.636 


3.506 


3.385 




54 


3.746 


3.677 


3.609 


3..544 


3.420 


3.3' '4 




59 


3.599 


3.534 


3.471 


3.410 ; 


3.294 ; 


3.184 




64 


3.388 


3.329 


3.272 j 


3.216 j 


3.111 ' 


3.011 




69 


3.105 


3.054 


3.004 1 


2.956 


2.863 ; 


2.776 




74 


2.749 


2.707 


2.666 


2.626 


2.550 


2.478 




79 


2.327 


2.295 


2.264 


2.234 


2.175 


2.119 


80 


10 i 


3.770 


3.700 


3.632 


3.567 


3.442 


3.325 




15 j 


3.766 


3.696 


3.629 


3.563 


3.439 


3.322 




20 


3.760 


3.690 


3.623 


3.558 


3.433 


3.317 




25 


3.752 1 


3.682 i 


3.615 


3.550 


3.426 


3.310 




30 


3.741 1 


3.672 


3.605 


3.540 


3.417 


3.301 




35 


3.727 1 


3.658 


3..591 


3.527 


3.404 


3.289 




40 


3.706 


3.638 1 


3.572 


3.508 


3.387 


3.272 




45 


3.667 


3.600 


3,535 


3.473 


3.353 


3.241 




50 


3.602 


3.537 


3.474 


3.413 


3.297 


3.187 




55 


3.505 


3.443 


3.383 


3.325 


3.213 


3.109 




60 


3.364 


3.306 


3.250 


3.195 


3.091 


2.993 




65 


3.162 


3.109 


3.058 


3.009 


2.914 


2.825 




70 


2.892 


2.846 


2 802 


2.759 


2.677 


2.599 




75 


2..553 


2.516 


2.480 


2.445 


2.377 


2.313 




80 


2.152 

1 


2.124 


2.096 


2.0G9 


2.017 


1.968 


81 


1 
11 j 


3.526 


3.464 


3.403 


3 345 


3.233 


3.128 




16 [ 


3.522 


3.460 


3.400 


3.341 1 


3.230 


3.125 




21 1 


3.516 


3.454 


3.394 


3.336 ■■ 


3.225 


.3.120 



TASXiB XXXI. 

LIFE ANNUITIES— JOINT LIVES. 

Shewing the Values of Annuities on Two Joint Lives according to 
the combined experience of various Life Offices. 



Age. 


2| 
Per Cent. 


3 

Per Cent. 


3^ 4 
Per Cent. Per Cent. 

1 


5 

Per Cent. 


6 
Per Cent. 


Older. 


Younger. 


SI 


26 


3.509 


3.447 


3.387 


3.329 


3.218 


3.113 




31 


3.499 


3.437 


3.377 


3.320 


3.209 


3.105 




36 


3.485 


3.424 


3.365 


3.307 


3.197 


3.094 




41 


3.465 


3.405 


3.346 


3.289 


3.180 


3.078 




46 


3.426 


3.367 


3.309 


3.253 


3.146 


3.046 




51 


3.364 


3.306 


3.250 


3.196 


3.092 


2.994 




56 


3.272 


3.217 


3.164 


3.112 


3.012 


2.918 




61 


3.137 


3.085 


3.035 


2.987 


2.894 


2.806 




66 


2.944 


2.897 


2.852 


2.808 


2.724 


2.644 




71 


2.688 


2.648 


2.008 


2.570 


2.497 


2.428 




76 


2.366 


2.334 


2.302 


2.270 


2.210 


2.153 




81 


1.985 


1.961 


1.936 


1.913 


1.867 


1.823 


QZ 


12 


3.288 


3.233 


3.179 


3.127 


3.028 


2.934 




17 


3.285 


3.229 


3.176 


3.124 


3.025 


2.931 




22 


3.279 


3.224 


3.171 


3.119 


3.020 


2.926 




27 


3.272 


3.217 


3.164 


3.112 


3.013 


2.920 




32 


3.263 


3.208 


3.155 


3.104 


3.005 


2.912 




37 


3.250 


3.196 


3,143 


3.092 


2.994 


2.902 




42 


3.231 


3.177 


3.125 


3.074 


2.977 


2.886 




47 


3.193 


3.140 


3.089 


3.039 


2.944 


2.854 




52 


3.134 


3.082 


3.033 


2.984 


2.892 


2.805 




57 


3.046 


2.998 


2.950 


2.904 


2.815 


2.732 




62 


2.917 


2.871 


2.827 


2.784 


2.701 


2.623 




67 


2.734 


2.693 


2.653 


2.614 


2.539 


2.468 




72 


2.492 


2.456 


2.421 


2.388 


2.323 


2.261 




77 


2.187 


2.158 


2.130 


2.103 


2.050 


1.999 




82 


1.826 


1.804 


1.783 


1.762 


1.722 


1.684 


S3 


13 


3.055 


3.007 


2.959 


2.913 


2.825 


2.742 




18 


3.052 


3.003 


2.956 


2.910 


2.822 


2.739 




23 


3.047 


2.998 


2.951 


2.906 


2.818 


2.734 




28 


3.040 


2.992 


2.945 


2899 


2.812 


2.729 




33 


3.032 


2.983 


2.937 


2.891 


2.804 


2.721 




38 


3.020 


2.972 


2.926 


2.881 


2.794 


2.712 




43 


3.001 


2.954 


2.908 


2.863 


2.777 


2.696 




48 


2.964 


2.918 


2.873 


2.829 


2.745 


2.665 




53 


2.908 


2.863 


2.820 


2 777 


2.695 


2.618 




58 


2.826 


2.783 


2.741 


2-700 


2.622 


2.548 




63 


2.703 


2.663 


2.624 


2.586 


2.513 


2.444 




68 


2.530 


2.494 


2 459 


2.425 


2.359 


2.296 




73 


2.302 


2.271 


2.241 


2.211 


2.154 


2.099 




78 


2.015 


1.990 


1.9G5 


1.941 


1.894 


1.850 




83 


1.673 


1.654 


1.636 


1.618 


1.582 


1.549 


8^ 


14 


2.826 


2.784 


2.742 


2.702 


2.624 


2.551 




19 


2.823 


2.781 


2 739 


2.699 


2.621 


2.548 




24 


2.819 


2.776 


2735 


2.695 


2.617 


2.544 




29 


2.813 


2.770 


2.729 


2.689 


2.612 


2.539 




34 


2.805 


2.762 


2.721 


2.682 


2.605 


2.532 




39 


2.794 


2.752 


2.711 


2.672 


2.595 


2.523 




44 


2.775 


2.734 


2.693 


2.654 


2.579 


2.507 



TABZiS ZZZZ. 

LIFE ANNUITIES— JOINT LIVES. 

Shewino- the Values of Annuities on Two Joint Lives according to 
the combined experience of various Life Offices. 



Age. 


2| _ 


3 


3.i 


4 


1 
5 i 


.. 1 


1,. Per Cent.JPer Cent.ll'er Uent.lJfer i^eni.rer uem. rer ueni.| 


Older. 1 


founger. 








i 


1 




84 


49 i 


2.740 


2.700 


2.660 


2.622 


2.548 


2.477 




54 


2.688 


2.648 


2.610 


2.573 


2.501 


2.4.33 




59 


2.610 


2.573 


2.536 


2.500 


2.432 


2.366 




64 


2.494 


2.459 


2.425 


2.392 


2.328 


2.267 




69 


2.333 


2.301 


2.270 


2.240 


2.182 


2.127 




74 


2.119 


2.092 


2065 


2.039 


1.989 


1.941 




79 


1.850 


1.828 


1.806 


1.785 


1.744 


1.705 




84 


1.525 


1.509 


1.493 


1.477 


1.447 


1.417 


85 


15 


2.G00 


2.563 


2.527 


2.492 


2.424 


2..360 




20 


2.597 


2.5G0 


2.524 


2.489 


2.421 


2.357 




25 


2.593 


2.556 


2.520 


2.485 


2.418 


2.354 




30 


2.587 


2.551 


2.515 


2.480 


2.413 


2 340 




35 


2.580 


2.544 


2.508 


2.473 


2.406 


2.343 




40 


2.570 


2.534 


2.499 


2.464 


2.398 


2.334 


45 ! 


2.552 


2.516 


2.481 


2.447 


2.381 


2.318 




50 


2.519 


2.484 


2.4.50 


2.416 


2.352 


2.290 




55 


2.470 


2.436 


2.403 


2..370 


2.308 


2.248 




60 


2.398 


2.365 


2.333 


2.302 


2.242 


2.185 




65 


2.290 


2.259 


2.229 


2.201 


2.145 


2091 




70 


2.139 


2.112 


2.085 


2.059 


2.008 


1.960 




1 

75 


1.940 


1.917 


1.894 


1.871 


1.828 


1.786 




80 


1.689 


1.670 


1.652 


1.633 


1.598 


1.564 




85 


1.381 


1.367 


1.353 


1.339 


1.313 


1.288 


86 


16 


2.376 


2.344 


2.313 


2.283 


2.225 


2.169 




21 


2.373 


2.342 


2.311 


2.280 


2.222 


2.166 




26 


2.370 


2.338 


2.307 


2.277 


2.219 


2.163 




31 


2.365 


2.333 


2.302 


2.272 


2.214 


2.159 




36 


2.358 


2.327 


2.296 


2.266 


2.208 


2.153 




41 


2.349 


2318 


2.287 


2.258 


2.200 


2.145 




46 


2.331 


2.300 


2.270 


2.241 


2.184 


2.129 




51 


2.301 


2.271 


2.241 


2.212 


2.157 


2.103 




56 


2.256 


2.227 


2.198 


2.170 


2.116 


2.064 




61 


2.188 


2.160 


2.133 


2.106 


2 055 


2.005 




66 


2 088 


2.062 


2.037 


2.012 


1.964 


1.918 




71 


1.950 


1.926 


1.903 


1.881 


1.837 


1.796 




76 


1.766 


1.746 


1.726 


1.707 


1.669 


1.633 




81 


1.534 


1.518 


1.502 


1.486 


1.456 


1.426 




86 

1 


1.2.39 


' 1.228 


1.216 


1.205 


1.182 


! 1.161 


87 


1 
17 


2.154 


'; 2.127 


2.101 


2.075 


2.025 


1.977 




22 


2.152 


j 2.125 


2.099 


2.073 


2.023 


1.975 




27 


2.149 


2.122 


2.095 


2.070 


2.020 


1.972 




32 


2.144 


2.117 


2.091 


2.065 


2.016 


1.968 




37 


2.139 


2.112 


2.086 


1 2.060 


2.011 


1.963 




42 


2.130 


2.104 


2.078 


j 2.052 


2.003 


1.956 




47 


2.113 


2.r87 


2.061 


1 2.036 


1.987 


1.941 




52 


2.085 


2.060 


2.034 


j 2.010 


1.962 


1.917 




57 


2.044 


] 2.019 


1.995 


1 1.971 


1.925 


1.881 




62 


1.982 


1 1.958 


1.935 


i 1.912 


1.868 


1.826 




67 


1.S91 


' 1.868 


' 1.847 


1.825 


1.784 


1.745 



TABX.S XIIZ, 

LIFE ANNUITIES— JOINT LIVES. 

Shewing the Values of Annuities on Two Joint Lives according to 
the combined experience of various Life Offices. 



Age. 


2i 
Per Cent. 


3 

Per Cent. 


"2 

Per Cent. 


4 
Per Cent. 


5 
Per Cent. 


6 
Per Cent. 


Older. 


Younger. 


87 


72 


1.764 


1.744 


1.725 


1.705 


1.668 


1.633 




77 


1.596 


1.579 


1.562 


1.545 


1.513 


1.482 




82 


1.383 


1.370 


1.356 


1.342 


1.316 


1.291 




87 


1.101 


1.092 


1.082 


1.072 


1.054 


1.036 


Q& 


18 


1.935 


1.912 


1.890 


1.868 


1.826 


1.786 




23 


1.933 


1.910 


1.888 


1.866 


1.824 


1.784 




28 


1.930 


1.907 


1.885 


1.863 


1.822 


1.781 




33 


1.926 


1.903 


1.881 


1.860 


1.818 


1.778 




38 


1.921 


1.899 


1.877 


1.855 


1.813 


1.773 




43 


1.913 


1.891 


1.869 


1.848 


1.806 


1.766 




48 


1.897 


1,875 


1.854 


1.832 


1.791 


1.752 




53 


1.872 


1.851 


1.830 


1.809 


1.769 


1.730 




58 


1.835 


1.814 


1.794 


1.774 


1.735 


1.697 




63 


1.779 


1.759 


1.739 


1.720 


1.683 


1.647 




68 


1.696 


1.678 


1.659 


1.641 


1.607 


1.573 




73 


1.582 


1.565 


1.549 


1.533 


1.501 


1.471 




78 


1.430 


1.415 


1.401 


1.387 


1.360 


1.334 




83 


1.236 


1.225 


1.213 


1.202 


1.180 


1.158 




88 


0.966 


0.958 


0.950 


0.942 


0.927 


0.912 


B9 


19 


1.719 


1.700 


1.682 


1.664 


1.629 


1.595 




24 


1.717 


1.698 


1.680 


1.662 


1.627 


1.593 




29 


1.714 


1.696 


1.677 


1.659 


1.625 


1.591 




34 


1.711 


1.692 


1.674 


1.656 


1.621 


1.588 




39 


1.707 


1.688 


1.670 


1.652 


1.617 


1.584 




44 


1.699 


1.681 


1.663 


1.645 


1.611 


1.577 




49 


1.685 


1.667 


1.649 


1.631 


1.597 


1 .564 




54 


1.663 


1.645 


1.627 


1.610 


1.577 


1.545 




59 


1.630 


1.612 


1.595 


1.579 


1.546 


1.515 




64 


1.579 


1.563 


1.546 


1.530 


1.499 


1.470 




69 


1.506 


1.490 


1.475 


1.460 


1.431 


1.403 




74 


1.404 


1.390 


1.376 


1.363 


1.337 


1.311 




79 


1.268 


1.256 


1.244 


1.232 


1.210 


1.188 




84 


1.093 


1.083 


1.074 


1.064 


1.046 


1.028 




89 


0.834 


0.828 


0.821 


0.815 


0.802 


0.790 


90 


20 


1.508 


1.492 


1.477 


1.463 


1.434 


1.407 




25 


1.506 


1.491 


1.476 


1.461 


1.433 


1.405 




30 


1.504 


1.489 


1.474 


1.459 


1.431 


1.403 




35 


1.501 


1.486 


1.471 


1.456 


1.428 


1.401 




40 


1.497 


1.482 


1.467 


1.453 


1.424 


1.397 




45 


1.490 


1.475 


1.461 


1.446 


1.418 


1.391 




50 


1.478 


1.463 


1.448 


1.434 


1.406 


1.379 




55 


1.458 


1.444 


1.430 


1.415 


1.388 


1.362 




60 


1.439 


1.415 


1.401 


1.388 


1.361 


1.336 




65 


1.385 


1.371 


1.358 


1.345 


1.320 


1.295 




70 


1.320 


1.308 


1.295 


1.283 


1.259 


1.237 




75 


1.231 


1.220 


1.209 


1.197 


1.176 


1.155 




80 


1.111 


1.101 


1.092 


1.082 


1.063 


1.045 




85 


0.954 


0.946 


0.938 


0.930 


0.915 


0.900 




90 


0-708 


0.703 


0.697 


0.692 


0.682 


0.673 



TABZiXS XZV. 

ABSOLUTE REVERSIONS— PRESENT VALUES. 

Shewinrr the Present Value of£l, to be received at the end of the 
year m %vhich an Assigned Life may fail, according to the Mortalitv 
obtained from the combined experience of various Life Offices 



Age. 
10 


4 
•rCent 


5 
W Cent. 


6 
W Cent. 


Age. 


4 
#• Cent. 


5 
W Cent. 



#* Cent. 


.21331 


.16401 


.13131 


55 


.53932 


.47253 


.41727 


11 


.21fi58 


.16658 


.13328 


56 


.55115 


.48490 


.42994 


12 


.219.2 


.16930 


,13544 


57 


.56312 


.49762 


.44285 


13 


.22341 


.17211 


.13770 


58 


.57515 


.51039 


.45597 


14 


.22707 


.17506 


.14002 


59 


.58727 


.52333 


.46934 


15 


.23084 


.17816 


.14252 


60 


.59943 


.53643 


.48286 


16 


.23476 


.18135 


.14517 


61 


.61162 


.54959 


.49063 


17 


.23884 


.18472 


.14789 


62 


.62385 


.56277 


.51045 


18 


.24303 


.18820 


.15077 


63 


.63600 


.57606 


.52436 


19 


.24742 


.19187 


.15377 


64 


.64811 


.58929 


.53834 


20 


.25188 


.19568 


.15695 


65 


.66019 


.60254 


.55238 


21 


.25657 


.19963 


.16022 


66 


.67211 


.61572 


.56641 


22 


.26138 


.20373 


.16368 


67 


.68396 


.62882 


.58039 


23 


.26634 


.20801 


.16724 


68 


.69566 


.64186 


.59432 


24 


.27149 


.21244 


.17104 


69 


.70720 


.65472 


.60820 


25 


.27680 


.21707 


.17494 


70 


.71858 


.66749 


.62201 


26 


.28229 


.22187 


.17907 


71 


.72977 


.68011 


.63565 


27 


.28798 


.22687 


.18338 


72 


.74077 


.69254 


.64918 


28 


.29384 


.23206 


.18791 


73 


.75159 


.70477 


.66253 


29 


.29991 


.23743 


.19260 


74 


.76216 


.71682 


.67573 


30 


.30614 


.24306 


.19752 


75 


.77251 


.72862 


.68874 


31 


.31261 


.24886 


.20262 


76 


.78265 


.74024 


.70153 


32 


.31931 


.25491 


.20801 


77 


.79254 


.75162 


.71415 


33 


.32615 


.26118 


.21361 


78 


.80219 


.76276 


.72649 


34 


.33327 


.26772 


.21950 


79 


.81157 


.77362 


.73860 


35 


.34061 


.27452 


.22560 


80 


.82072 


.78423 


.75044 


36 


.34816 


.28150 


.23200 


81 


.82965 


.79462 


.76204 


37 


.35600 


.28891 


.23868 


82 


.83835 


.804>^] 


.77347 


38 


.36408 


.29653 


.24570 


83 


.84693 


.81482 


.78474 


39 


.37242 


.30447 


.25306 


84 


.85535 


.82471 


.79595 


40 


.38104 


.31271 


.26075 


85 


.86369 


.83458 


.80710 


41 


.38996 


.32134 


.26879 


86 


.87200 


.84438 


.81830 


42 


.39918 


.33028 


.27728 


87 


.88022 


.85414 


.82945 


43 


.40869 


.33962 


.28611 


88 


.88843 


.86391 


.84055 


44 


.41849 


.34923 


.29540 


89 


.89650 


.87357 


.85164 


45 


.42857 


.35925 


.30497 


90 


.90444 


.88306 


.86257 


46 


.43884 


.36948 


.31487 


91 


.91216 


.89233 


.87332 


47 


.44934 


.38000 


.32512 


92 


.91962 


.90134 


.88374 


48 


.46004 


.39077 


.33565 


93 


.92070 


.90992 


.89366 


49 


.47088 


.40176 


.34646 


94 


.93320 


.91782 


.90287 


50 


.48192 


.41306 


.35762 


95 


.93908 


.92496 


.91120 


51 


.49311 


.42452 


.36899 


96 


.94378 


.93068 


.91792 


52 


.50446 


.43620 


.38065 


97 


.94743 


.93510 


.92309 


53 


.51597 


.44810 


.39258 


98 


.95231 


.94106 


.93004 


54 


.52759 


.46020 


.40481 











TABX.S XV. 

LIFE ASSURANCES— SINGLE LIVES. 

Shewing the Single and Annual Premium for the Assurance of £1 on 
a Single Life, according to the Mortality obtained from the combined 
exjierlence of various Life Offices, reckoning Interest at 3 per cent. 





Single 


Annual 




Single 


Annual 


Age. 


Premium. 


Premium. 


Age. 


Premium. 


Premium. 


]0 


.29061 


.01193 


55 


.62075 


.04767 


11 


.29456 


.01216 


56 


.63139 


.04988 


12 


.29863 


.01240 


67 


.64205 


.05224 


13 


.30284 


.01265 


58 


.65274 


.05474 


14 


.30718 


.01291 


59 


.66344 


.05741 


15 


.31165 


.01318 


60 


.67414 


.06025 


16 


.316-25 


.01347 


61 


.68480 


.06328 


17 


.32099 


.01376 


62 


.69541 


.06649 


18 


.32585 


.01408 


63 


.70595 


.06992 


19 


.33086 


.01440 


64 


.71640 


.07357 


20 


.33600 


.01473 


65 


.72673 


.07745 


21 


.34128 


.01508 


66 


.73694 


.08159 


22 


.34669 


.01545 


67 


.74700 


.08599 


23 


.35226 


.01583 


68 


.75689 


.09068 


24 


.35797 


.01624 


69 


.76662 


.09567 


25 


.36383 


.01665 


70 


.77617 


.10100 


26 


.36985 


.01709 


71 


.78553 


.10668 


27 


.37603 


.01755 


72 


.79469 


.11274 


28 


.38236 


.01803 


73 


.80364 


.11921 


29 


.38886 


.01853 


74 


.81239 


.12612 


30 


.39552 


.01905 


75 


.82092 


.1.3352 


31 


.40235 


.01960 


76 


.82923 


.14143 


32 


.40936 


.02018 


77 


.83732 


.14991 


33 


.41654 


.02079 


78 


.84518 


.15900 


34 


.42389 


.02143 


79 


.85281 


.16875 


35 


.43144 


.02210 


80 


.86021 


.17924 


36 


.43917 


.02280 


1 81 


.86740 


.19053 


37 


.44710 


.02355 


82 


.87440 


.20278 


38 


.45524 


.02434 


83 


.88126 


.21616 


39 


.46358 


.02517 


! 84 


.88799 


.23091 


40 


.47214 


.02605 


85 


.89465 


.24734 


41 


.48093 


.02698 


86 


.90123 


.26577 


42 


.48995 


.02797 


87 


.90774 


.28658 


43 


.49919 


.02903 


88 


.91419 


.31029 


44 


.50863 


.03014 


89 


.92053 


.33740 


45 


.51826 


.03133 


90 


.92673 


.36837 


46 


.52804 


.03258 


91 


.93276 


.40404 


47 


.53795 


.03391 


92 


.93857 


.44498 


48 


.54798 


.03530 


93 


.94405 


.49143 


49 


.55812 


.03678 


94 


.94910 


.54302 


50 


.56836 


.03835 


95 


.95362 


.59885 


51 


.57870 


.04000 


96 


.95726 


.65219 


52 


.58912 


.04176 


97 


.96005 


.70014 


53 


.59960 


.04361 


98 


.96382 


.77558 


54 


.61015 


.04558 









TABZ.S XVZ. 

LIFE ASSURANCES— JOINT LIVES. 

Shewing the Single and Annual Premium required to secure a Sum 
paj^able at the decease of the first of Two Assigned Lives, accordino- 
to the combined experience of various Life Offices, reckoning interest 
at 3 per Cent. 



Age. 




Annual Annual 


Single 




Age. 


Annual 


Annual Single 






I 

1 

2 


'remium Prem. 
3er Cent, per £1. 


Prem. 
per £1 






. Premiun 
per Cent 


1 Prem. Prem. 


Older. 


Younger 


Older. 

27 


Younger 


, per £1 


per £1 


14 


14 


11 


i .02044 


.41238 


12 


2 7 


7 


.0237C 


1 .44958 
















17 


2 9 





.0244^ 


.45665 


15 


10 


2 





.02000 


.40719 




22 


2 10 


11 


02546 


.46641 




15 


2 


1 7 


.02080 


141673 




27 


2 13 


8 


02685 


.47966 


16 


11 


1 


8 


.02035 


.41137 


2S 


13 


2 8 


8 


.024.32 


.45503 




16 


o 


2 5 


.02119 


.42121 




18 
23 


2 10 
2 12 


1 
1 


02504 
.02606 


.46227 
.47227 


17 


12 
17 


2 
2 


1 5 
3 2 


.02072 
.02160 


41567 
.42585 




28 


2 15 


1 


.02753 


.48587 














29 


14 


2 9 


9 


.02487 


.46062 


18 


13 


2 


2 2 


.02110 


.42014 




19 


2 11 


3 


.02563 


.46804 




18 


2 


4 


.02202 


43059 




24 
29 


2 13 
2 16 


5 
6 


.02070 
.02823 


.47827 
.49222 


19 


14 


2 


3 


.02150 


.42474 


1 














19 


2 


4 11 


.02247 


.43548 


1 30 


10 
15 


2 9 

2 10 


10 
11 


.02493 
.02545 


.46117 
.46638 


20 


10 


2 


2 5 


.02121 


.42139 




20 


2 12 


6 


.02624 


.47398 




15 


2 


3 10 


.02192 


.42946 




25 


2 14 


9 


.02737 


.48444 




2J 


2 


5 10 


.02293 


.44053 


1 

1 


30 


2 18 





.02898 


.49872 


21 


11 


2 


3 3 


.02161 


.42600 


31 


11 


2 11 





.02551 


.46693 




16 


2 


4 9 


.02236 


.43432 




16 


2 12 


2 


.02607 


.47230 




21 


2 


6 10 


.02342 


44568 




21 
26 


2 13 
2 16 


9 
2 


.02689 
.02807 


.48007 
.49076 


ZZ 


12 
17 


2 
2 


4 1 

5 8 


.02204 
.02282 


.43074 
.43930 




31 


2 19 


6 


.02976 


.50539 




22 


2 


7 10 


.02392 


45097 


32 


12 
17 


2 12 
2 13 


3 
5 


.02613 
.02671 


.47288 
.47840 


23 


13 


2 


5 


.02248 


.43563 




22 


2 15 


2 


.02758 


.48631 




18 


2 


6 7 


.02329 


.44442 




27 


2 17 


7 


.02880 


.49723 




23 


2 


8 11 


.02445 


•45642 




32 


3 1 


2 


.03058 


.51220 


24 


14 


2 


5 1, 


.02294 


44067 


33 


13 


2 13 


7 


.02678 


47900 




19 


2 


7 7 


.02380 


.44972 




18 


2 14 


9 


.02739 


.48462 




24 


2 


10 


.02501 


46201 




23 

28 


2 16 
2 19 


7 
2 


.02829 
.02958 


.49272 
.50.387 


25 


10 
15 


2 
2 


5 7 

6 10 


.02281 
.02343 


•43918 
.44586 




33 


3 2 


11 


03145 


.51919 




20 


2 


8 8 


.02433 


.45515 


34 


14 


2 14 


11 


02746 


.48529 




25 


2 


11 2 


.02559 


.46775 




19 
24 


2 16 
2 18 


2' 
1 


02810 
02904! 


.49102 
49927 


2.C 


11 


2 


6 7 


.02329 


.44431 




29 


3 


9 


03039 


.51068 




16 


2 


7 11 


.02395 


.45118 




34 


3 4 


9 


03237 


52635 




21 


2 


9 9 


02488 


.46071 
















26 


2 


12 5 


.02621 


.47363 


35 


10 ' 


2 15 


5 

1 
1 


02771 


48759 



LIFE ANNUITIES— JOINT LIVES. 

Shewing the Single and Annual Premium required to secure a Sum 
payable at the decease of the first of two Assigned Lives, according 
to the combined experience of various Life Offices, reckoning Interest 
at 3 per Cent. 



Ag( 




Annual ^ 


Annual 


Single 


Age. 


Annua 


Annual Single 1 




I 

founger. ' 


'remium 

er Cent. 

1 
1 


Prem. Prem. 
per £1. per £1. 


] 


Premium Prem. Prem. 
jer Cent, per £1. per £1. 


Oider. "5 


Older. "' 


f ounger* ^ 


35 


15 5 


2 16 4 . 


02818 


49175 


^1 


36 


3 15 


2 . 


1 
03759 .56344 




20 ' 


2 17 8 . 


02885 


49761 




41 


4 1 


l'. 


04054 .58192 




25 


2 19 8 .02983 


50599 








1 


1 




30 


3 2 6.03126 


51768 


42 


12 


3 6 10 .03343 .534401 




35 


3 6 8. 


03333 


53369 




17 
22 


3 7 
3 9 


9 .03387 .53762 
.03452 .54234 


36 


11 


2 16 11 


02845 


.49414 




27 


3 10 


11 .03544 .54887 




16 


2 17 11 ! 


02894 


.49840 




32 


3 13 


8 .03682 .55830 




21 


2 19 3! 


02964 


.50437 




37 


3 17 


9 .03889 .57177 




26 


3 14! 


.03067 


.51290 




42 


4 4 


1 .04204 .59075 




31 


3 4 4' 


.03217 


.52480 








1 1 




36 


3 8 9 


.03436 


.54120 


43 


13 


3 9 


.03452 .54235 


37 












18 


3 10 


.03498 .54564 


12 


2 18 6 


.02923 


.50088 




23 


3 11 


4 .03565 .55039 




17 


2 19 6 


.02974 


.50521 




28 


3 13 


3 


.03662 .55700 




22 


3 10 


.03048 


.51130 




33 


3 16 


2 


.03808.56658 




27 


3 3 1 


.03155 


.51997 




38 


4 


7 


.04028.58033 




32 


3 6 3 


.03313 


.53214 




43 


4 7 


4 


.04366.59981 




37 


3 10 11 


.03545 


.54893 
























44 


14 


3 11 


4 


.03567 


.55050 


38 


13 


3 1 


.03005 


.50780 




19 


3 12 


4 


.03616 


.55385 




18 


3 12 


.03059 


.51224 




24 


3 13 


9 


.03686 


.55862 




23 


3 2 8 


.03135 


.51840 




29 


3 15 


9 


.03788 


.56533 




28 


3 5 


.03248 


.52724 




34 


3 18 


10 


.03941 


.57506 




33 


3 8 4 


.03415 


.53966 




39 


4 3 


6 


.04176 


.58910 




38 


3 13 2 


.03660 


.55685 




44 


4 10 


9 


.04537 


.60904 


39 


14 


3 1 10 


.03092 


.51493 


45 


10 


3 13 


1 


.03655 


.55654 




19 


3 3 


.03149 


.51945 




15 


3 13 


10 


.03690 


.55887 




24 


3 4 7 


.03228 


.52571 




20 


3 14 


10 


.03741 


.56224 




29 


3 7 


.03348 


.53471 




25 


3 16 


4 


.03815 


.56704 




34 


3 10 5 


.03522 


.54739 




30 


3 18 


5 


.03921 


.57381 




39 


3 15 8 


.03783 


.56499 




35 


4 1 


8 


.04084 


.58371 














40 


4 6 


8 


.04333 .59803 


40 


10 
15 


3 2 11 
3 3 8 


.03145 
.03184 


.51916 
.52227 


j 


45 


4 14 


5 


.04721 .61845 




20 


3 4 10 


.03243 


.52688 


46 


11 


3 15 


8 


.03783 .56501 




25 


3 6 6 


.03327 


.53323 




16 


3 16 


5 


.03820 .56736 




30 


3 9 


.03452 


.54238 




21 


3 17 


6 


.03873 .57079 




35 


3 12 9 


.03(137 


.55531 




26 


3 19 





.03950 .57561 




40 


3 18 3 


.03914 


.57335 




31 


4 1 


3 


.04063 .58246 












j 


36 


4 4 


8 


.04235 


.59250 


%l 


11 


3 4 10 


.03241 


.52667 




41 


4 10 





.04501 


i. 607 15 




16 


3 5 8 


.03283 


.52985 




46 


4 18 


4 


.04917 


1.62798 




21 


3 6 11 


.0334/: 


.53451 
















26 


3 8 8 


.03432 


. .54095 


47 


12 


3 18 


5 


.03919 


.57363 




31 


3 11 3 


.03562 


i .55024 


1 


17 


3 19 


2 


.03957 


.57602 



TABX.E XVI. 

LIFE ASSURANCES— JOINT LIVES. 

Shewing the Single and Annual Premium required to secure a Sum 
payable at the decease of the first of two Assigned Live?, according 
to the combined experience of various Life Offices, reckoning Interest 
at 3 per Cent. 



A 


;e. 


An mi 


al 


Annual Sinsjle 


Age 


A 


nnui 


ii 


Annual 


Single 






Premium 
per Cent. 


Prem. ' Prem. 
per £l.'per £1. 




Premium 
per Cent. 


Prem. 
per £1. 


Prem. 
per £1. 


Older. 


Younger- 


Older. 


Younger. 


4:7 


22 


4 





3 


1 
.04013 .57943 


52 


22 


4 


15 


5 


.04772 


.62008 




27 


4 


1 


11 


.04094 .58429 




27 


4 


16 


10 


.04842 


.62442 




32 


4 


4 


3 


.04212 .59122 




32 


4 


18 


11 


.04946 


.02938 




37 


4 


7 


11 


.04395 .60140 




37 


5 


2 


1 


.05105 


.03071 




42 


4 


13 


7 


.04680 .61641 




42 


5 


7 


2 


.05359 


.64787 




47 


5 


2 


6 


.05124 .63755 




47 
52 


5 

6 


15 

7 


4 

4 


.05766 
.06367 


.66438 
.68615 


48 


13 


4 


1 


3 


.04062 .58240 


















18 


4 


2 





.04102 .58479 


53 


13 


4 


17 


7 


.04879 


.62615 




23 


4 


3 


3 


.04161 .58823 




18 


4 


18 


3 


.04915 


.62790 




28 


4 


4 


10 


.04246 .5931 1 




23 


4 


19 


4 


.04965 


.03028 




33 


4 


7 


5 


.04371 


.60011 




28 


5 





9 


.05039 


.63372 




38 


4 


11 


4 


.04565 


.01046 




33 


5 


3 





.0.5148 


.63867 




43 


4 


17 


5 


.04871 


.62583 




38 


5 


6 


4 


.05317 


.64609 




48 


5 


6 


10 


.05343 


.64720 




43 

48 


5 
6 


11 



10 
6 


.05591 
.00026 


65748 
.07414 


•£9 


14 
19 


4 
4 


4 
5 


3 

1 


.04213 
.04255 


.59128 
.59366 




53 


6 


13 


4 


.06665 


.69596 




24 


4 


6 


4 


.04317 


.59710 


5€ 


14 


5 


1 


7 


.05079 


.63552 




29 


4 


8 


1 


.04406 


.60202 




19 


5 


2 


4 


.05117 


.63726 




34 


4 


10 


9 


.04538 


.60910 




24 


5 


3 


5 


.05169 |.C3962| 




39 


4 


14 


11 


.04745 


.61964 




29 


5 


4 


11 


.05247 


.64306 




44 


5 


1 


6 


.05075 


.63535 




34 


5 


7 


3 


.05362 


.64801 




49 


5 


11 


6 


.05577 


.65690 




39 
44 


I 


10 
16 


10 
9 


.05543 
.05839 


.65556 
.66718 


50 


10 


4 


6 


10 


.04343 


.59856 




49 


6 


G 





.06301 


.68389 




15 


4 


7 


6 


.04374 


.60028 




54 


6 


19 


8 


.06983 


.70566 




20 


4 


8 


4 


.04418 


.60266 


















25 


4 


9 


8 


.04482 


.60610 


55 


10 


5 


5 


3 


.05263 


.64374 




30 


4 


11 


6 


.04576 


.61104 


1 


15 


5 


5 


10 


.05292 


.64499 




35 


4 


14 


4 


.04716 


.61822 




20 


5 


6 


8 


.05332 


.64671 




40 


4 


18 


9 


.04937 


.62894 




25 


5 


7 


9 


.05387 


.64907 




45 


5 


5 


10 


.0.5291 


.64496 




30 


5 


9 


5 


.05469 


.65247 




50 


5 


16 


6 


.05824 


.66663 


1 


35 

40 


5 
5 


11 
15 


10 

8 


.05590 
.05784 


.65745 
.66508 


51 


11 


4 


10 


3 


.04511 


.60764 




45 


6 


2 


1 


.06103 


.67693 




16 


4 


10 


11 


.04544 


.C0939 




50 


6 


11 


11 


.06596 


.69369 




21 


4 


11 


10 


.04590 


.61178 




55 


7 


6 


5 


.07321 


.71538 




26 


4 


13 


2 


.04657 


.61522 


















31 


4 


15 


1 


.04756 


.02017 


56 


11 


5 


9 


9 


.05487 


.65323 




36 


4 


18 


1 


.04905 


.62743 




16 


5 


10 


4 


.05518 


.65450 




41 


5 


2 


10 


.05141 


.63835 




21 


5 


11 


2 


.05559 


.65619 




46 


5 


10 


5 


.05521 


.65465 




26 


5 


12 


4 


.05617 


.65853 




51 


6 


1 


9 


.06088 


.67638 




31 

36 


5 
5 


14 
16 


1 
8 


.05703 
.05832 


.66194 
.66692 


52 


12 


4 


13 


9 


.04689 


.61684 




41 


6 





10 


.06041 


.67469 


17 


4 


14 


6 


.04724 


.61859 




46 


6 


7 


8 


.06385 


.68673 



T^BZiS XVI. 



LIFE ASSURANCES— JOINT LIVES. 

Shewing the Single and Annual Premium required to secure a Sum 
payable at the decease of the first of two Assigned Lives, according 
to the combined experience of various Life Offices, reckoning Interest 
at 3 per cent. 



Age. 


Annual i 


4.niiual 


Single 


Age. 


Annual 


iinnual Single 1 




] 


Premium 
)er Cent. 


Prem. Prem. , . 
per £. per £1.1 

i 




Premium Prem. 1 Prem. 
per Cent, per £1. per £1. 


Older. 1 


^ounger. I 


Older. Younger. 


56 


51 ( 


3 18 2 


06909 


70344 


61 


11 


6 16 4 


06817 . 


70065 




56 


7 13 7 


07681 


72505 

1 




16 
21 


6 16 11 
6 17 8 


06844 
06883 


70146 
70266 


57 


12 


5 14 6 


05725 


66278' 




26 


6 18 8 


.06935 


70422 




17 


5 15 2 


.05758 


664061 




31 


7 2 


.07009 


70644 




22 


5 16 


.05801 


.66575 




36 


7 2 5 


.07121 


.70973 




27 


5 17 3 


.05862 


.66805 




41 


7 6 1 


.07304 


.71492 




32 


5 19 


.05952 


.67143 




46 


7 12 4 


.07616 


.72336 




37 


6 1 9 


.06089 


.67644 




51 


8 1 11 


.08096 


.73542 




42 


6 G 4 


.06315 


.68437 




56 


8 16 4 


.08815 


.75164 




47 


6 13 8 


.06684 


.69651 




61 


9 17 9 


.09888 


.77246 




52 


7 4 10 


.07242 


.71317 














57 


8 13 


.08064 


.73466 


62 


12 

17 


7 2 10 
7 3 5 


.07142 
.07170 


.71031 
.71113 


58 


13 


5 19 7 


.05978 


.67239 




22 


7 4 3 


.07211 


.71229 




18 


6 3 


.06018 


.67367 




27 


7 5 4 


.07266 


.71384 




23 


6 1 2 


.06059 


.67534 




32 


7 6 11 


.07344 


.71602 




28 


6 2 5 


.06122 


.67763 




37 


7 9 3 


.07463 


.71928 




33 


6 4 4 


.06217 


.68098 




42 


7 13 3 


.07662 


.72456 




38 


6 7 3 


.06364 


.68603 




47 


7 19 11 


.07997 


.73303 




43 


6 12 2 


.06608 


.69409 




52 


8 10 2 


.08509 


.74500 




48 


7 1 


.07004 


.70629 




57 


9 5 6 


.09277 


.76105 




63 


7 11 11 


.07597 


.72287 




62 


10 8 6 


.10426 


.78164 




58 


8 9 6 


.08475 


.74424 






















63 


13 


7 9 9 


.07487 


.71992 


59 


14 


6 5 


.06249 


.68207 




18 


7 10 4 


.07517 


.72074 




19 


6 5 8 


.06284 


.68331 ! 




23 


7 11 2 


.07559 


.72188 




24 


6 6 8 


.06332 


.68495' 




28 


7 12 4 


.07618 


.72342 




29 


6 8 


.06399 


.68723 




33 


7 14 


.07699 


.72555 




34 


6 10 


.06499 


.69054 




38 


7 16 6 


.07827 


.72881 




39 


6 13 2 


.06657 


.69563 




43 


8 11 


.08044 


.73417 




44 


6 18 5 


.06922 


.70385 




48 


8 8 1 


.08404 


.74261 




49 


7 6 11 


.07345 


.71605 




53 


8 19 


.08949 


.75447 




54 


7 19 6 


.07977 


.73254 




58 


9 15 5 


.09771 


.77037 




. 59 


8 18 4 


.08915 


.75374 




63 


11 


.11000 


.79064 


60 


10 


6 10 3 


.06511 


.69095 


6^ 


14 


7 17 1 


.07855 


.72951 




15 


6 10 8 


.06537 


.09176 




19 


7 17 9 


.07888 


.73032 




20 


6 11 C 


.06574 


.69299 




24 


7 18 8 


.07932 


.73145 




25 


6 12 C 


.06624 


.69459 




29 


7 19 IC 


.07993 


.73292 




30 


6 13 11 


.06695 


.69683 




34 


8 1 7 


.08079 


.73501 




35 


|6 16 C 


.0680C 


.70015 




39 


8 4 4 


■ .08216 


.73827 




40 


|6 19 5 


.0697C 


.70528 




44 


8 9 C 


.08452 


.74372 




45 


7 5 2 


.07257 


.71360 




49 


8 16 £ 


.08838 


.75214 




50 


7 14 2 


! .0770S 


1 .72578 




54 


9 8 £ 


.09421 


.76385 




55 


8 7 8 


S .0838? 


( .74215 




59 


10 6 C 


1 .10298 


.77952 




60 


9 7 £ 


) .0938e 


» .76318 




64 


11 12 £ 


t .11611 


.79946 



TABZ.E XVZ. 

LIFE ASSURANCES— JOINT LIVES. 

Shewing the Single and Annual Premium required to secure a Sum 
payable at the decease of the first of two Assigned Lives accordinir 
to the combined experience of various Life Offices, reckoning Interest 
at 3 per Cent. ° 



Age. 


Annual 


Annual 


Single 


Age. 


Annual 


Annua] 


$>iric7]a 




. Premium 
per Cent. 


Prem. 
per £1. 


Prem. 
per £1. 




Premium 
per Cent. 


Prem. 
per ^1 


oiiigit; 


Older. 

65 


Younger 


Older. 


Younger 


Prem. 
per £1 




10 


8 4 6 


.08224 


.73848 


68 


13 


9 11 


1 


.09554 


.76038 






15 


8 4 11 


.08247 


.73900 




18 


9 11 


8 


.09582 


.76691 


V 




20 


8 5 7 


.08281 


.73982 




23 


9 12 


5 


.09621 


.76763 






25 


8 6 6 


.08327 


.74087 




28 


9 13 


5 


.09673 


.76859 






30 


8 7 10 


.08390 


.74232 




33 


9 14 


11 


.09747 


.76993 






35 


8 9 8 


.08483 


.74442 




38 


9 17 


2 


.09857 


.77191 






40 


8 12 7 


.08629 


.74765 




43 


10 1 





.10049 


.77529 






45 


8 17 9 


.08888 


.75319 




48 


10 7 


6 


.10376 


.78083 






50 


9 6 


.09300 


.76152 




53 


10 17 


6 


.10877 


.78878 






55 


9 18 5 


.09922 


.77308 




58 


11 12 


8 


.11635 


.79979 






60 


10 17 3 


.10861 


.78855 




63 


12 15 


10 


.12791 


.81453 






65 


12 5 4 


.12266 


.80812 




68 


14 9 


11 


.14497 


.83270 




66 


11 


8 12 10 


.08640 


.74788 


€9 


14 


10 1 


1 


.10056 


.77541 






16 


8 13 4 


.08665 


.74844 




19 


10 1 


9 


.10086 


.77593 






21 


8 14 


.08700 


.74920 




24 


10 2 


6 


.10126 


.77663 






26 


8 15 


.08749 


.75024 




29 


10 3 


7 


.10181 


.77757 






31 


8 16 3 


.08814 


.75164 




34 


10 5 


o 


.10259 


.77888 






36 


8 18 3 


.08912 


.75.368; 




39 


10 7 


6 


.10376 


.78083 






41 


9 15 


.09072 


.756971 




44 


10 11 


9 


.10586 


.78423 






46 


9 7 


.09352 


.76254; 




49 


10 18 


9 


.10937 


.78971 






51 


9 15 10 


.09792 


.77075; 




54 


11 9 


5 


.11472 


.79752 






56 


10 9 1 


.10456 


.78214; 




59 


12 5 


8 


.12285 


.80835 






61 


11 9 3 


.11464 


.79740 




64 


13 10 


5 


.13521 


.82277 






66 


12 19 3 


.12968 


.81654 




69 


15 6 


9 


.15339 


.84042 




67 


12 


9 1 8 


.09084 


.75721 


70 


10 


10 11 


5 


.10569 


.78397 






17 


9 2 2 


.09109 


.75773J 




15 


10 11 


10 


.10591 


.78432 






22 


9 2 11 


.09147 


.75849! 




20 


10 12 


5 


.10622 


.78482 






27 


9 3 11 


.09197 


.75948 




25 


10 13 


4 


.10667 


.78552 






32 


9 5 4 


.09267 


.76088 




30 


10 14 


6 


.10724 


.78042 






37 


9 7 5 


.09370 


.76288 




35 


10 16 


1 


10804 


.78767 






42 


9 10 10 


.09543 


76G18 




40 


10 18 


8 


10932 


78962 






47 


9 16 11 


.09847 


.77174 




45 


11 3 


3.11162 


79306 






52 


10 6 4 


.10317 


77984 




50 


11 10 


9 .115.38 


79845 






57 


11 6' 


.11027 


79105 




55 


12 2 


2 .12109 


80610 






62 


12 2 2 


12107 


80608 




60 


12 19 


7 .12980 


81674 






67 


13 14 l' 


13704 . 


82472 




65 


4 6 


.14302 


83081 




[ 












70 1 


6 4 


9.16237 


84791 





TABXiS XVXX. 

LIFE ASSURANCES— LAST SURVIVOR. 

Shewing the Single and Annual Premium required to secure a Sum 
payable at the extinction of the last survivor of two Assigned Lives 
according to the combined experience of various Life Offices, reckoning 
Interest at 3 per Cent. 



A 


ge. 


Annual 


Annual 


Single 


Age. 


Annual Annual 


Single 






Premium 
per Cent. 


Prem. 
per £\. 


Prem. 
per £1. 






Premium 
per Cent. 


Prem. 
per £1. 


Prem. 
per £1. 


Older 


Young(!r 


Older. 


Younger 


14 


14 


14 9 


.00737 


.20198 


27 


12 
17 


16 11 
18 5 


.00846 
.00921 


.22510 
.24036 


15 


10 


14 1 


.00705 


.19509 




22 


1 1 


.01004 


.25633 




15 


15 2 


.00758 


.20662 




27 


1 1 10 


.01090 


.27241 


16 


11 


14 


.00725 


.19947 


28 


13 


17 5 


.00871 


.23020 




16 


15 7 


.00780 


.21133 




18 
23 


19 

1 9 


.00959 
.01036 


.24596 
.26238 


17 


12 
17 


14 11 
16 1 


.00746 
.00803 


.20396 
.21613 




28 


1 2 6 


.01126 


.27888 












29 


14 


17 11 


.00896 


.23544 


18 


13 


15 4 


.00767 


.20856 




19 


19 7 


.00979 


.25170 




18 


16 6 


.00827 


.22113 




24 
29 


I 1 5 
13 3 


.01069 
.01164 


.26859 
.28553 


19 


14 


15 9 


.00789 


.21331 














19 


17 


.00851 


.22624 


30 


10 
15 


16 11 
18 C 


.00844 
.00923 


.22496 
.24080 


20 


10 


15 


.00752 


,20525 




20 


1 2 


.01010 


.25755 




15 


16 3 


.00813 


.21823 




25 


1 2 1 


.01104 


.27491 




20 


17 6 


.00877 


.23150 




30 


1 4 1 


.01203 


.29234 


21 


11 


15 6 


.00773 


.20988 


31 


11 


17 5 


.00870 


.23000 




16 


16 9 


.00837 


.22324 




16 


19 


.00952 


.24634 




21 


18 1 


.00903 


.23690 




21 
26 


1 10 

1 2 10 


.01042 
.01140 


.26358 
.28147 


ZZ 


12 
17 


15 11 
17 3 


.00795 
.00862 


.21461 
.22839 




31 


1 4 11 


.01244 


.29935 




22 


18 8 


.00932 


.24243 


32 


12 

17 


17 11 
19 7 


.00895 
.00981 


.23512 
.25196 


23 


13 


16 5 


.00819 


.21949 




22 


I 1 6 


.01075 


.26975 




18 


17 9 


.00888 


.23369 




27 


1 3 7 


.01179 


.28817 




23 


19 3 


.00961 


.24811 




32 


1 5 9 


.01287 


.30651 


24 


14 


16 10 


.00843 


.22450 


33 


13 


18 5 


•00921 


.24039 




19 


18 4 


.00915 


.23911 




18 


1 3 


.01011 


.25778 




24 


19 10 


.00991 


.25394 




23 

28 


1 2 2 
1 4 5 


.01110 
.01219 


.27610 
.29507 


25 


10 
15 


16 
17 4 


.00799 
.00868 


.21526 
.22965 




33 


1 6 8 


.01332 


.31388 




20 


18 10 


.00943 


.24471 


34 


14 


19 


.00948 


.24578 




25 


1 5 


.01022 


.25991 




19 
24 


1 10 
1 2 11 


.01043 
.01147 


.26373 
.28261 


26 


11 


16 5 


.00822 


.22013 




29 


1 5 3 


.01261 


.30208 




16 


17 11 


.00897 


.23495 




34 


1 7 7 


.01379 


.32143 




21 


19 6 


.00973 


.25045 














26 


1 1 1 


.01056 


.26609 


35 


10 


17 10 


.00890 


23445 



TABZ.E XVZX. 

LIFE ASSURANCES— LAST SURVIVOR. 

Shewing the Single and Annual Premium required to secure a Sum 
payable at the extinction of the last survivor of two Assigned Lives, 
according to the combined experience of various Life Offices, reckoning 
Interest at 3 per Cent. 



Age. 



Older. 



35 



Younger. 



Annual 
Premium 
per Cent. 



36 



37 



38 



39 



40 



41 



15 
20 
25 
30 
35 

11 
16 

21 
26 
31 
36 

12 
17 
22 
27 
32 
37 

13 
18 
23 
28 
33 
38 

14 
19 
24 
29 
34 
39 

10 
15 
20 
25 
30 
35 
40 

n 

16 

I 21 

26 

31 



19 7 

1 1 6 
13 8 
1 6 I 

1 8 7 



Annual j Single 



Prem. 
per £1. 



18 




2 3 

4 

7 
9 



Prem. 
per£I. 



Age. 



Older. Younger. 



.00977 .25135 
.01076 .26984 
.01185 .28927 
.01304 .30928 
.01429 .32917 



00917 .23961 

010071.25706 

0111l!.27610 

6j.01225'. 29615 

0.01350|. 31673 

7 .014811.33716 



18 11 



41 



42 



.00944' 



91.010381 
2 111.01147! 
5 4.01267 
7 11 01398; 
10 9.01536 



19 5 .00972 



115 
1 3 8 
16 3 
19 
1 11 10 

10 



01071 
01184 
.01311 
.01448 
01593 



1 2 
1 4 
;i 7 

|l 10 
|1 13 

18 



.24489 

.26288 

.28252 

.30316; 

.32431 

.34528 

.25031 
.26889 
.28913 
.31039 
;. 33215 
35367 



OlOOl 25583 
01104 .27500 
012231.29586 
,01356i.31775 
.01500.34010 
.01654 .36220 



1 8 


1. 


1 11 


2 


1 14 


4 


19 


4 


1 1 


3 


|1 3 


6 


1 6 


2 


,1 9 

i 


1 



9 .009381.24360 
.01031 i.26153 
.011391.28130 
.012641.30276 
01404 .32529 
01557 1.34828 
01718'.37097 



00965 '.24885 
,01002. 26736 
,011761.28772 
,01308 '.30986 
.01454.33308! 



43 



44 



45 



46 



47 



36 

41 

12 
17 
22 
27 
32 
37 
42 

13 
18 
23 
28 
33 
38 
43 

14 
19 
24 
29 
34 
39 
44 

10 
15 
20 
25 
30 
35 
40 
45 

11 
16 
21 
26 
31 
36 
41 
46 

12 
17 



Annual Annual 
Premium Prtm. 
per Cent, per £1. 



1 12 4^.01615 
1 15 8.01784 



Single 
Prem. 
per £1 



19 10 .00992 



1 

4 

7 

10 

13 

17 



11 .01095 
3 .01214 

.01352 
2 .01 507 
6 .01676 

1 .01855 



5 .01021 
7 .01129 
1 .01254 
.01399 
3 .01562 
14 10 .01741 
18 7 .01929 




2 
5 

8 
11 



1 
3 
5 
9 
12 
16 




10 19 
1 1 



4 

6 

10 

13 

17 



.01051 
3 .01164 
11 .01296 
.01448 
5 .01620 
2 .01809 
2 .02009 

8.00983 
8 .01083 
01.01201 
9i. 01339 
0|.01500 
8 .01681 
71.01880 



.35670 
.37997 

.2.5421 
.27331 
.2943-2 
.31712 
.34101 
.36529 
.38914 

.25968 
.27941 
.30107 
.32457 
.34916 
.37411 
.39855 

.2a533 
.28567 
.30800 
.33221 
.35748 
.38314 
.40825 

.25234 
.27107 
.29204 
.31.505 
.33998 
.36599 
.39237 



2 1 10 .020921.41807 





2 

4 

7 

11 1 
14 11 



19 
3 


3 



2'.01010' 

4.01115 

9 .01239 

8 .01385 

01554 

,01745 

,01956 

.02180 



9.01039 
0.01149 



.25761 
.27695 
.29856 
.32230 
.34796 
.37472 
.40185 
; 42812 

'.26296 
.28293 



TAB]:.E XVIZ. 

LIFE ASSURANCES— LAST SURVIVOR. 

Shewing the Single and Annual Premium required to secure a Sum 
payable at the extinction of the last survivor of^ two Assigned Lives 
according to the combined experience of various Life Offices, reckoning 
Interest at 3 per Cent. 



Ag 


e. 


Annual 


fVnnual 


Single 


Age. 


Annual 


Annual 


Single 






Premium 
per Cent. 


Prem. 
per £1. 


Prem. 
per £1. 




Premium 

per Cent. 


Prem. 
per £1. 


Prem. 
per £1. 


Older. ' 


ifounger. 


Older. ^ 


ifounger. 


47 


22 


1 5 7 


.01279 


.30522 


sz 


22 


1 6 


9 


.01338 


.31484 




27 


1 8 8 


.01432 


.32969 




27 


I 10 


1 


.01505 


.34074 




32 


1 12 2 


.01610 


.35609 




32 


1 14 


1 


.01704 


.36910 




37 


1 16 3 


.01812 


.38363 




37 


1 18 


9.019371 


.39952 




42 


2 9 


.02036 


.41149 




42 


2 4 


2 


.02208 


.43121 




47 


2 5 6 


.02273 


.43834 




47 
52 


2 10 
2 16 


2 
6 


.02508 
.02822 


.46269 
.49211 


48 


13 


1 1 4 


.01068 


.26845 
















18 


1 3 8 


.01184 


.28907 


53 


13 


1 2 


3 


.01112 


.27632 




23 


1 6 5 


.01321 


.31205 




18 


1 4 


8 


.01233 


.29758 




28 


1 9 8 


.01482 


.33727 




23 


1 7 


7 


.01380 


.32160 




33 


1 13 5 


.01670 


.36444 




28 


1 11 


1 


.01556 


.34828 




38 


1 17 8 


.01884 


.39279 




33 


1 15 


4 


.01766 


.37748 




43 


2 2 5 


.02120 


.42136 




38 


2 


3 


.02013 


.40878 




48 


2 7 5 


.02371 


.44879 




43 

48 


2 6 
2 12 



5 


.02300 
.02619 


.44131 
.47346 


49 


14 
19 


1 2 
1 4 5 


.01099 
.01220 


.27404 
.29533 




53 


2 19 





.02951 


.50331 




24 


1 7 3 


.01364 


.31900 


.54 


14 


1 2 


10 


.01141 


.28182 




29 


1 10 8 


.01534 


.34499 




19 


1 5 


5 


.01270 


.30374 




34 


1 14 8 


.01732 


.37292 




24 


1 8 


6 


.01424 


.32849 




39 


1 19 2 


.01958 


.40208 




29 


1 12 


2 


.01609 


.35597 




44 


2 4 2 


.02210 


.43144 




34 


1 16 


8 


.01831 


.38602 




49 


2 9 6 


.02474 


.45936 




39 
44 


2 1 

2 7 


10 
11 


.02093 
.02398 


.41819 
.45162 


50 


10 


10 6 


.01025 


.26040 




49 


2 14 


9 


.02736 


.48439 




15 


12 7 


.01131 


.27976 




54 


3 1 


9 


.03088 


.51463 




20 


1 5 2 


.01258 


.30170 
















25 


1 8 2 


.01409 


.32609 


55 


10 


1 1 


3 


.01064 


.26763 




30 


1 11 9 


.01587 


.35283 




15 


1 3 


6 


.01174 


.28743 




35 


1 15 11 


.01797 


.38157 




20 


1 6 


2 


.01308 


.31007 




40 


2 9 


.02038 


.41157 




25 


1 9 


5 


.01470 


.33552 




45 


2 6 1 


.02303 


.44166 




30 


1 13 


4 


.01665 


.36380 




50 


2 11 8 


.02583 


.47008 




35 
40 


1 18 

2 3 



6 


.01900 
.02177 


.39474 
.42783 


51 


11 


1 1 1 


.01053 


.26562 




45 


2 10 





.02502 


.46207 




16 


1 3 3 


.01164 


.28558 




50 


2 17 


2 


.02859 


.49542 




21 


1 5 11 


.01297 


.30820 




55 


3 4 


8 


.03233 


.52612 




26 


1 9 1 


.01456 


.33334 
















31 


1 12 11 


.01644 


.36089 


56 


11 


1 1 


10 


.01092 


.27273 




36 


1 17 4 


.01865 


.39046 




16 


1 4 


2 


.01208 


.29315 




41 


2 2 5 


.0212C 


.42130 




21 


1 6 


11 


.01348 


.31647 




46 


2 8 1 


.02408 


.45208 




26 


1 10 


4 


.01518 


.34272 




51 


2 14 C 


.0269£ 


1 .48101 




31 
36 


1 14 
1 19 


6 
5 


.01723 
.01971 


.37181 
.40364 


52 


12 


1 1 e 


.01085 


t .27092 




41 


2 5 


4 


.02266 


.43764 




17 


1 4 C 


) .0119t 


) .29151 




46 


2 12 


3 


.02611 


.47270 



TABXiS XVZZ, 

LIFE ANNUITIES— LAST SURVIVOR. 

Shewing the Single and Annual Premiums required to secure a Sum 
payable at the extinction of the Last survivor of Two Assigned Lives 
according to the combined experience of various Life Offices, reckoning 
Interest at 3 per Cent. 



Age. 


A 


nnual 


Annual 


Single 


Age. 


Annual 


Annual 


Single 






Premium 
per Cent. 


Prem. 
for £1. 


Prem. 
for £1. 




Premium 
per Cent. 


Prem. 
for £1. 


Prem. 
for £\. 


Older. 


Younger. 


Older. 


Younger. 


56 


51 


2 


19 


10 


.02991 


.50664 


61 


16 


1 4 


11 


.01246 


.29962 




56 


3 


7 


9 


.03387 


.53771 




21 
26 


I 7 
1 10 


10 
5 


.01392 
.01571 


.32344 
.35043 


57 


12 




2 


5 


.01121 


.27792 




31 


1 15 


10 


.01790 


.38072 




17 




4 


10 


.01242 


.29897 




36 


2 1 


2 


.02060 


.41425 




22 




7 


9 


.01389 


.32300 




41 


2 7 


10 


.02390 


.45082 




27 




11 


4 


.01568 


.35003 




46 


2 15 


10 


.02792 


'.48949 




32 




15 


8 


.01784 


.37997 




51 


3 5 


2 


.03259 


.52807 




37 


2 





11 


.02046 


.41270 




56 


3 15 


6 


.03776 


.56454 




42 


2 


7 


2 


.02360 


.44762 




61 


4 6 


4 


.04317 


.59713 




-47 


2 


14 


6 


.02726 


.48349 
















52 


3 


2 


7 


.03130 


.51800 


62 


12 


1 3 


1 


.01153 


.28377 




57 


3 


11 





.03551 


.54942 




17 
22 


1 5 

I 8 


7 

8 


.01279 
.014.33 


.30528 
.32984 


58 


13 




3 





.01150 


.28319 




27 


1 12 


5 


.01621 


.35702 




18 




5 


6 .01277 


.30490 




32 


1 17 





.01852 


.38877 




23 




8 


8 .014.32 


.32966 




37 


2 2 


9 


.02136 


.42325 




28 




12 


5 .01620 


.35748 




42 


2 9 


9 


.02489 


.46082 




33 




16 


11 


.01848 


.38829 




47 


2 18 


4 


.02916 


.50034 




38 


2 


2 


6 


.02126 


.42198 




52 


3 8 


3 


.03412 


.53955 




43 


2 


9 


2 


.02458 


.45782 




57 


3 19 


3 


.0.3962 


.57643 




48 


2 


16 


11 .02848 


.49443 




62 


4 10 


10 


.04540 


.60922 




53 


2 


5 


6 .03277 


.52946 
















58 


3 


14 


6 


.03725 


.56121 


63 


13 
18 


1 3 

1 6 


8 
4 


.01183 
.01315 


.28887 
.31105 


59 


14 




3 


7 


.01181 


.28858 




23 


1 9 


6 


.01476 


.33035 




19 




6 


3 


01314 


.31100 




28 


1 13 


6 


.01673 


.36490 




24 




9 


6 


.01477 


.33649 




33 


1 18 


4 


.01917 


.39694 




29 




13 


8 


.01675 


.36512 




38 


2 4 


4 


.02217 


.43240 




34 




18 


4.01916 


.39681 




43 


2 11 


10 


.02592 


.47095 




39 


2 


4 


2!. 02209 


.43141 




48 


3 


11 


.03047 


.51133 




44 


2 


11 


31.02564 


.46825 




53 


3 11 


6 


.03575 


.55108 




49 


2 


19 


6.02977 


.50553 




58 


4 3 


3 


.04162 


.58831 




54 


3 


8 


8 


.03433 


.54105 




63 


4 15 


6 


.04777 


.62124 




59 


3 


18 


2 


.03910 


.57316 


64: 


14 


1 4 


3 


.01213 


.29409 


60 


10 




1 


11 


.01098 


.27381 




19 


1 7 





.01351 


.31693 




15 




4 


3 


.01213 


.29406 




24 


1 10 


5 


.01520 


.34295 




20 




7 


1 


.01352 


.31717 




29 


1 14 


7 


.01728 


.37237 




25 




10 


6'. 01523 


.34339 




34 


1 19 


8 


.01984 


.40528 




30 




14 


8.01731 


.37283 




39 


2 6 


1 


.02304 


.44172 




35 




19 


9:. 01986 


.40542 




44 


2 14 





.02702 


.48133 




40 




6 


0'. 02298 


.44102 




49 


3 3 


9 


.03185 


.52239 




45 


•2 


13 


6 .02676 


.47879 




54 


3 14 


11 


.03747 


.56270 




50 


3 


2 


3 .03114 


.51671 




59 


4 7 


6 


.043751.60034 1 




55 


3 


12 


.03598 


.55274 




64 


5 


7 


.05030 


.633341 




60 


4 


2 


2 .X)4107 


.58511 


























65 


10 


1 2 


6 


.01126 .27888 


61 


11 


1 


2 


6 .01125 


.27873 




15 


1 14 


11 


.01245 .29940 














I 















TA8LS XVXX. 

LIFE ANNUITIES— LAST SURVIVOR. 

Shewing the Single and Annual Premiums required to secure a Sum 
payable at the extinction of the last Survivor of two Assigned Lives 
according to the combined experience of various Life Offices, reckoning 
Interest at 3 per Cent. 



Age. 


Annual 


Annual 


Single 


Age. 


Annual 


Annual 


S ingle 




_ 


Premium 
per Cent. 


Prem. 
for £1. 


Prem. 
for£l. 




Premium 
per Cent. 


Prem. 
for £1. 


Prem. 
for jei. 


Older, i Younger. 


Older. 


Younger, 


65 


20 


1 7 


9 


.01389 


.32295 


68 


18 


1 6 


11 


.01344 


.31583 




25 


1 11 


4 


.01566 


.34971 




23 


1 10 


2 


.01510 


.34153 




30 


1 15 


8 


.01785 


.37994 




28 


1 14 


3 


.01714 


.37068 




35 


2 1 


1 


.02055 


.41376 




33 


1 19 


5 


.01970 


.40350 




40 


2 7 


11 


.02395 


.45124 




38 


2 5 


10 


.02291 


.44024 




45 


2 16 


4 


.02818 


.49182 




43 


2 13 


11 


.02697 


.48078 




50 


3 6 


7 


.03331 


.53357 




48 


3 4 


2 


.03207 


.52405 




55 


3 18 


7 


.03931 


.57442 




53 


3 16 


6 


.03824 


.56772 




60 


4 12 





.04600 


.61233 




58 


4 11 





.04552 


.60983 




65 


5 6 





.05300 


.64537 




63 
68 


5 7 

6 4 


5 
5 


.05369 
.06219 


.64830 
.68107 


66 


11 


1 3 


1 


.01153 


.28363 
















16 


1 5 


6 


.01276 


.30476 


69 


14 


I 4 


9 


.01239 


.29839 




21 


1 8 


7 


.01428 


.32903 




19 


1 7 


7 


.01380 


.32154 




26 


1 12 


3 


.01613 


.35655 




24 


1 11 


3 


.01554 


.34796 




31 


1 16 


10 


.01843 


.38764 




29 


1 15 


5 


.01769 


.37792 




36 


2 2 


7 


.02130 


.42244 




34 


2 


9 


.02037 


.41163 




41 


2 9 


10 


.02490 


.46091 




39 


2 7 


6 


.02377 


.44937 




46 


2 18 


10 


.02941 


.50244 




44 


2 16 


2 


.02809 


.49102 




51 


3 9 


9 


03487 


.54489 




49 


3 7 





.03351 


.53503 




56 


4 2 


6 


.04127 


.58619 




54 


4 


2 


.04009 


.57926 




61 


4 16 


10 


.04840 


.62434 




59 


4 15 


9 


.04787 


.62172 




66 


5 11 


9 


.05587 


.65733 




64 
69 


5 13 

6 11 


2 

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LEGAL DECISIONS 



ON 



LIFE ASSURANCE! 

A DIGEST OF 

ALL THE REPORTED CASES, 

CHRONOLOGICALLY ARRANGED. 



Ross versus Bradshaw. 

Trinity Term, 17G1. 
Concealment of circumstances on a life insurance is not so fatal if the 
life be warranted good, as if it be a common insurance. " Where there is 
a warranty, then nothing need be told ; but it must in general be proved, 
if litigated, that the life was in fact a good one, and so it may be 
though he have a particular infirmity. The only question is, whether 
he was in a reasonably good state of health, and such a life as ought to 
be insured on common terms."-— Lord Mansfield. 1. W. Black. 312. 
See also on this pointy Willis versus Poole. 2 Park on Ins. 935. 



Stackpole versus Simon. 

Hilary Vac. 1779. 
Where a Broker, who effected an insurance, told the Underwriters 
that the person for whom he acted would not warrant, but he believed 
the party to be a good life. Held, that the Underwriters were liable. 
2 Park on Ins. 932. 



Patterson versus Black. 

Hilary Vac. 1780. 
Where an insurance is made upon the life of a man who goes to sea, 
and the ship in which he sailed is never afterwards heard of, the question 



whether he did or did not die within the term insured, is a fact for the 
Jury to ascertain from the circumstances which shall be produced in 
evidence before them. 2 Park on Ins. 920. 

LocKYER versus Offley. 

2Qth Maij,\im. 
On an Insurance on a man's life for a year, if, some short time before 
the expiration of the term, he receives a mortal wound, of which he 
dies after the year, the insurer will not be liable. — 1. T. R. 260. — ■ 
A supposed case by Willes, J. 



DwYER versus Edie. 

Hilarij Term, 1788. 
The holder of a note given for money won at play, has not au insur- 
able interest in the life of the maker of the note. 2 Park on Ins. 914. 



TiDSWELL versus Ankerstein. 

An executor in trust has a sufficient interest to enable him to make 
assurance in his own name, on the life of a person who has granted an 
annuity to the testator. Peahens N. P. 204. 

Anderson versus Edie. 

Trinity Term, 1795. 
A bona fide creditor has such an interest in his debtor's life, that he 
may insure it and recover upon the policy. 2 Park on Ins. 915. 



AvESON versus Lord Kinnaird, and others. 

Qth Feb. 1805. 
In an action by the husband upon a policy of insurance on the life 
of his wife, declarations by his wife, made by her when lying in bed, 
apparently ill, stating the bad state of her health at the period of her 
going to M. (whither she went a few days before in order to be exam- 
ined by a surgeon, and to get a certificate from him of good health, 
preparatory to making the insurance) down to that time, and her ap- 
prehensions that she could not live ten days longer, by which time the 
policy was to be returned, are admissible in evidence to shew her own 
opinion, who best knew the fact of the ill state of her health at the time 
of effecting the policy, which was on a day intervening between the 



time of her going to M. iind the day on whicli such decUirations were 
made ; and particularly after the plaintiff had called the surgeon as a 
witness to prove that she was in a good state of health when examined 
by him at M., this judgment being formed, in part, from the satis- 
factory answers given by her to his enquiries. 6 East, 188. 

Holland, Executor of O'Hara, versws Smith, Executor of Kendrick. 

4th March, 1806. 
Where a policy of insurance has been effected on the life of a debtor, 
as a security to the lender of money, and the lender charges the pre- 
miums to the account of the debtor, who pays them, if the principal 
is afterwards paid, the debtor, or his representative, is entitled to the 
policy. 6 Esp. 11. 



GoDSALL and others^ versus Boldero and others, Directors of the 
Pelican Life Insurance Company, 

2oth Nac.imi. 
A Creditor may insure the life of his Debtor to the extent of his 
debt; but such a contract is substantially a contract of indemnity 
against the loss of the debt ; and therefore, if, after the death of the 
debtor, his executors pay the debt to the insuring creditor, the latter 
cannot afterwards recover upon the policy ; although the debtor died 
insolvent, and the executors were furnished with the means of payment 
by a third party. — 9 East, 72. 



Want and others, versus Blunt and others, Directors of a Life 
Assurance Society for the benefit of Widoios and Female Relatives. 

l-2th Feb. 1810. 
W here one, as a member of a Life Insurance Society for the benefit 
of widows and female relatives, entered into a Policy of Insurance with 
the society for a certain annuity to his widow after his death, in consi- 
deration of a quarterly premium to be paid to the Society during his 
life, and the Society covenanted with him and his executors, &c., that 
if he should pay to their clerk the quarterly premiums on the quarter- 
days during his life, and if he should also pay his proportion of contribu- 
tions, which the members of the Society should, during his life, be called 
on to make, in order to supply any deficiences in their funds, then, on 
due proof of his death, the Society engaged to pay the annuity to his 
widow ; and by the rules of the Society, if any member neglected to 



pay up the quarterly premiums for fifteen days after they were due, 
the policy was declared to be void, unless the member (continuing in as 
good health as when the policy expired) pay up the arrears within six 
months, and five shillings per month extra : — Held, that a member 
insuring, having died, leaving a quarterly payment over-due at the 
time of his death, the policy expired ; and that a tender of the sum by 
the member's executor, though made within fifteen days after it became 
due, did not satisfy the requisition of the policy and the rules of the 
Society which required such payment to be made by the member in 
his lifetime, continuing in as good health as when the policy expired. — 
12 Easty 183. 



"Watson versus Mainwabing and others, Directors of the Equitable 

Ir„surance Office. 

6th May, 1813. 

It is not to be concluded that a disorder with which a person is 
afflicted before he effects an insurance on his life is a "disorder tending 
to shorten life," within the meaning of the declaration required by the 
Equitable Insurance Office, from the mere circumstance that he after- 
wards dies of it, if it be not a disorder which generally has that 
tendency. — 4 Taunt. 763. 



HuGUENiN versus Raylby — the Albion Insurance Company. 

6th May, 1815. 
The conditions of a life insurance required a declaration of the state 
of the health of the assured, and the policy was to be valid only if the 
statement were to be free from all misrepresentation and reservation : 
the declaration described the assured as resident at Fisherton Anger ; 
she was then a prisoner in the county gaol there : — Held, that it was a 
question for the Jury whether the imprisonment were a material fact, 
and ought to have been communicated. — 6 Taunt., 186. 

HiGGiNS versus Sakgent and others. 

Nov. 1823. 
Interest is not recoverable in an action of covenant upon a policy of 
Assurance upon the life of A., by which a certain sum was made pay- 
able six months after due proof of his death, although the money in- 
sured was not paid at the time stipulated for that purpose. — 3 D. Sf JR. 
613. 2 B. Si- C. 348. 



Maynard versus Rhodes. 

SthNov.lB2A. 
Where an insurance was efFected on the life of A. for the benefit of B., 
and the Insurance Office acted upon A.'s own representation as to the 
state of his health, and it turned out that he was not an insurable life:— 
Held, that B. could not maintain an action on the policy, althou"-h he 
was not privy to the representation. 5 Dowl. and Ryl 266, 1 C. and 
P. 360. 



Morrison versus Mustpratt. 

^\it January, 18-27. 
A female upon whose life it was proposed to effect an insurance was 
represented to the insurers, in December, 1822, by A., a medical man, 
as enjoying^ ordinarilj', a good state of health. The same representa- 
tion was repeated by A. in March, and the insurance was effected in 
April, 1823. Between December, 1822, and March, 1823, she had 
been ill with a pulmonary attack, and was attended by B. ; but no 
disclosure of these circumstances was made to the insurers. In April, 
1824, she died of a pulmonary disease : — Held, on motion for a new 
trial, that the Jury ought to have been called on to consider whether 
the illness in 1823, and the attendance of B., ought to have been dis- 
closed to the insurers ; and that it was not sufficient to direct them 
generally to consider whether or not there had been any misrepresenta- 
tion.— 4 Bing, 60. 12 Moore, 231. 

BoLLAND versus Disney, tlie Amicable Assurance Society. 

2Ut May, 1827. 
In the policies effected by the Amicable Society, there is no exception 
as to death by the hands of justice. A person insuring his life in that 
office afterwards suffered death for a criminal offence, the policy was 
not thereby avoided. 3 Muss. 351. Bui see The Amicable Society App. 
Bolland and others, Resp. page 6. 

LiNDENAU versus Desborough, Secretary to the Atlas Insurance 

Company, 

\2th Nov. 1828. 
If the assured, at the time of effecting the policy, conceals anything 
material for the plaintiff to know, the policy is void ; and it matters 
not whether or not the assured considered it material or.not ; and what 



6 

amounts to a misrepresentation, or to a material concealment, is a 
question for the Jury 5 the fact that, on a life policy, an unusually 
high premium was paid, is quite immaterial, and therefore not to be 
taken as a proof that the Office considered the party to be a bad life. — 
3 31. Sc R., 45. 8 jB. ^ C. 586. 3 C. ^ P. 350. 



Everett versus Desborough, Secretary to the Atlas Insura^ice 

Company. 

21th May, 1829. 

1. — In an insurance upon the life of another, the life insured, if applied 
to for information, is, in giving such information, impliedly the Agent 
of the party insuring, who is bound by his statements, and must suffer 
if they are false, although he is unacquainted with the life insured, and 
the servant of the Insurance Office undertakes to do all that is required 
by his Office. 2. — Plaintiff effected an insurance on the life of H, with 
whom he was unacquainted, desired the Agent of the Insurance Office to 
do all that was requisite. The Agent knew H well, and made the usual 
inquiries. One of th e terms of the contract was, a reference to the usual 
Medical Attendant of the life insured. H. having given a false refer- 
ence : Held, that the Plaintiff could not recover. — 5 Bing, 503. M. 
and P. 190. 



The Amicable Society Appellants, James Bolland and others, 

Respondents. 

1830. 
H. F. assures his life in January, 1815, and pays premiums regulary 
till 1824. In June, 1815, H. F. commits a felony, of which he is con- 
victed in October, 1824, and for which he is executed in Nov. 1824. 
Bill filed in 1825, by the representatives of H. F., claiming under him 
and in his right, for payment of the sum alleged to be due on the In- 
surance, and decree in favour of the representatives : but the judgment 
reversed by the Lords, on the ground, that, by the general policy of the 
law, the insurance became void as to those claiming under and in right 
of H. F., in consequence of the death being occasioned by his own crim- 
inal act. 2 Dow and Clark, 1. 4 Bligh, N. S. 194. 



Richard Halford versus Kymer ajid others. Directors of the 
Asylum Life Insurance Company. 

Uh May, 1830. 
The stat. 14 Geo. 3, c. 48, s. 1, enacts that no insurance shall ha 



made on lives, or any other event, wherein the person for wliose bene- 
fit the policy shall he made shall have no interest ; and that every such 
assurance shall be void : and by s. 3, it is enacted that in all cases where 
the insured hath interest in such life or event, no greater sum shall be 
recovered or received from the insurers than the amount or value of the 
interest of the insured in such life or other event. In order to render 
a policy valid within the meaning of this Act, the party for whose be- 
nefit it is effected must have a pecuniary interest in the life or event 
insured ; and therefore a policj'^ eff'ected by a father on the life of his 
son, he not having any pecuniary interest therein, is void. — 10 B. and 
C. 724. 



J. G. S. Lepevre and others^ Trustees of the Promoter Life Assurance 
Company, versus Boyle. 

\^th January, 1832. 
A policy was effected by A. upon her own life with an Insurance 
Company: it was by deed, executed by three Trustees of the 
Company : A. afterwards assigned it to B. and died. The money due 
on the policy was paid to B. by a check drawn by the Trustees on the 
Bankers of the Company, and he gave an acknowledgment of having 
received the money from the Trustees. By the deed of trust the Board 
of Directors were to cause all monies belonging to the Company to be 
deposited wdth the Bankers in the name of the Trustees, and such 
monies were not to be withdrawn but for the purposes of the Compan j^, 
and by checks signed by the Trustees, or by three or more Directors 
under some authority to be given by the Trustees. After the payment 
to B. it was discovered that the policy was void on account of fraud : — 
Held, that, under the circumstances, the three Trustees were the proper 
plaintiffs in an action to recover back the monev so paid to B. — 3 B, Sf 
Add. ^11. 

SwETE versus Fairlie, and another, — tJie Globe Insurance Office. 

2Sth Feb, 1833. 
A policy of insurance on the life of another person, who, at the time 
of the insurance, is in a good state of health, is not vitiated by the non- 
communication by such person of the fact of his having, a few years 
before, been afflicted with a disorder tending to shorten life, if it ap- 
pear that the disorder was of such a character as to prevent the party 
from being conscious of what had happened to him while suffering 
under it- 6 C- and P- 1. 



Dtjckett — the Provident Life Assurance Company — versus Williams 
— the Hope Insurance Company. 

Hilary Term, 1834. 
Before effecting a policy of life insurance, a declaration and state- 
ment of health, and freedom from disease, &c., was signed by the 
assured. "By one clause it was stipulated that '• if any untrue averment 
was contained therein, or if the facts required to be set forth in the 
above proposal were not truly stated,'' the premiums were to be forfeited, 
and the assurance to be void. Held, that as the health, &c. of the party 
whose life was insured was untruly stated, though not to the knowledge 
of the party making the declaration and statement, the premiums, &c. 
were forfeited, and could not be recovered back. 2 Cramp, and Mees. 
348 4 Tyr. 240. 



Wainwright, Executor of Abercromhy, deceased, versus Bland 
and others, three of the Directors of tlie Imperial Life Assurance 
Company. 

'2,1th June, 1835. 
A party, on insuring her life, made false rei3resentations as to her 
object in effecting the insurance, and also as to her having obtained 
similar insurances from other offices, both of which facts were found by 
the Jury at the trial to be material to be known by the Insurance Com- 
pany. — Held, that the policy was thereby avoided, although such false 
representations were in answer to parol inquiries not comprised in the list 
of printed questions required by the regulations of the Office to be 
asked of the assured ; and although the policy, as framed, was only to 
be void on false answers being given to such printed questions. — 1 Tyr. 
Sf Gr. 417. 1 Moody a)id Rob. 481. 



Chattock versus Shawe and others, Directors of the Eagle Insurance 

Company. 

nth July, 1835. 
Where a policy of insurance contains a warranty that the assured 
^' has not been afflicted with, nor subject to, gout, vertigo, fits," &c. 
such warranty is not broken by the fact of the assured having had an 
epileptic fit in consequence of an accident. To vacate such policy it 
must be shown that the constitution of the assured was naturally liable 
to fits, or by accident or otherwise had become so liable. — 1 Moody S^ 
Bob. 498. 



9 

HucKMAN versus Fernie, Managing Director of the British 
Commei'cial Insurance Company. 

Easter Term, 1838. 
In an action on a Policy of Insurance effected by the plaintiff on the 
life of his wife, the declaration averred that the plaintiff had made 
statements (inter alia) that the wife was not afflicted with any disorder 
which tended to shorten life, and that she had led, and continued to lead, 
a temperate life. The defendant pleaded, that before the making of 
the policy, and on divers times after that day, the wife had been, and 
w^as afflicted with certain disorders, maladies or diseases— to wit, deli- 
rium tremens and erysipelatous inflammation of the legs, all which the 
plaintiff before, and at the time of making the policy, well knew. It ap- 
peared that at the time the policy was effected, the wife had been 
examined at the Insurance OfHce, and answered several questions put 
to her, but did not apprise the Company of her having been affected 
with those complaints. Tbe Jury found that the plaintiff had not any 
knowledge of her having had these disorders -.—Held, that upon the 
issue raised on these pleadings, the wife not being the general agent 
of the husband to effect the policy, but only sent to answer particular 
questions, her knowledge was not in this respect the knowledge of the 
husband. The wife had for several years been attended by A. B. up to 
her marriage with the plaintiff, and nearly to the time the policy was 
effected. After her marriage C. D., the medical attender of her husband's 
family, prescribed for her for a cold, or some trifling matter. In 
answer to the question put to her at the Ofiice, " who is your usual 
medical attendant," she replied, C. D.:— Held, that the learned Judge 
ought not to have left it to the Jury, on this evidence, to say which of 
the two was her usual medical attendant, but whether C. D. could be 
called her usual medical attendant at all. 3 Meeson 6f Welsby, 505. 



Rawlins, a Director of the Eagle Insurance Company, versus 
Desborough, Secretary to the Atlas Assurance Company. 

26th Feb. 1840. 
1. A party whose life is insured, is not the general agent for the assur- 
ed: and therefore the policy is not void by reason that such party failed 
to communicate a material fact, as to which he was not interrogated by 
the insurers, unless he was aware of the materiality of the fact and 



10 

studiously concealed it. 2. It is a question of fact for the Jury whether 
a fact, not communicated, was, under the circumstances, one which the 
assured ought to have communicated. — 2 Moody S^ Rob, 328, 



Craig, Bart, versus Fenn and others — the Asylum Life Insurance 

Company. 

WthBec. 1841. 
In an action against an Insurance Office on a life policy, it is no ob- 
jection to a Special Juror being sworn, that he is a director of another 
insurance office, unless that office has granted a policy on the life in 
question, and the amount of that policy be unpaid . 1 Carrand Marsh 
43. 

SouTHCOMBE versus Merriman, and others, Direcwrs of 

Life Insurance Company. 

nth March, 1842. 
Ill an action to recover the amount of a policy upon a life insurance, 
where the rules of the society stipulate that the insured shall be of 
sober and temperate habits, it is sufficient, on a plea denying the sober 
and temperate habits of the insured, for the defendants to shew that his 
habits were intemperate ; and it is no answer to this plea, that the 
plaintiff prove the intemperance not to have been to such a degree as to 
injure the health of the insured, or to shorten his life. 1 Carr and 
Mar. 286. ^^^ 




Jones and Caisston, Printers, 47, Eastcheap, London. 



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